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[]
[]
[]
[]
["Exam 5: Reserving E-02"]
[]
[]
[]
["Question","Sheet","Type"]
[1,1," Ratio method (additive) for S/S"]
[2,2," Apply reinsurance treaties and calculate net unpaid claims"]
[3,3," Additive or Multiplicative approach for ALAE"]
[4,4," Classical/Kittel approach for ULAE"]
[5,5," Congor & Nolibos approach for ULAE"]

{"sheet":"1","index":1,"n_rows":119,"n_cols":28,"rows_kept":119,"cut":false,"hidden":false,"merged":[]}
["Reading:",null,"Friedland 14 (S/S)",null,null,null,null,null,null,null,null,null,"Return to TOC","|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Model:",null,"2016.Fall #24(b)",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem Type:",null,"Ratio method (additive) for S/S",null,null,null,null,null,null,null,null,null,null,"|","Step 1:","Ratio of cumulative paid S/S to cumulative paid claims:",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem",null,"Use the","additive",null,"approach to estimate the",null,null,"unpaid","S/S","for AY",2020,null,"|",null,"AY",12,24,36,48,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P7-1","v":2017},{"$f":"ROUND(J10/D10,4)","v":2.8899999999999999E-2},{"$f":"ROUND(K10/E10,4)","v":3.5700000000000003E-2},{"$f":"ROUND(L10/F10,4)","v":3.5200000000000002E-2},{"$f":"ROUND(M10/G10,4)","v":3.5499999999999997E-2},null,null,null,null,null,null,null,"|"]
[null,null,"cumulative paid claims:",null,null,null,null,null,"cumulative paid SS:",null,null,null,null,"|",null,{"$f":"P8-1","v":2018},{"$f":"ROUND(J11/D11,4)","v":2.5100000000000001E-2},{"$f":"ROUND(K11/E11,4)","v":2.9600000000000001E-2},{"$f":"ROUND(L11/F11,4)","v":2.6200000000000001E-2},null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P9-1","v":2019},{"$f":"ROUND(J12/D12,4)","v":2.5899999999999999E-2},{"$f":"ROUND(K12/E12,4)","v":4.19E-2},null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY",12,24,36,48,null,"AY",12,24,36,48,"|",null,{"$f":"C13","v":2020},{"$f":"ROUND(J13/D13,4)","v":2.1000000000000001E-2},null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2017,6600,21800,31100,34600,null,2017,191,778,1095,1229,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2018,6500,21500,33900,null,null,2018,163,637,887,null,"|","Step 2:","Development triangle (multiplicative):",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2019,7900,21600,null,null,null,2019,205,904,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2020,7300,null,null,null,null,2020,153,null,null,null,"|",null,"AY",{"$f":"Q5&\"-\"&R5","v":"12-24"},{"$f":"R5&\"-\"&S5","v":"24-36"},{"$f":"S5&\"-\"&T5","v":"36-48"},{"$f":"T5&\"-\"&H9","v":"48-"},null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P6","v":2017},{"$f":"ROUND(IF($D$5=\"additive\",R6-Q6,R6/Q6),4)","v":6.7999999999999996E-3},{"$f":"ROUND(IF($D$5=\"additive\",S6-R6,S6/R6),4)","v":-5.0000000000000001E-4},{"$f":"ROUND(IF($D$5=\"additive\",T6-S6,T6/S6),4)","v":2.9999999999999997E-4},null,"  <===",{"$f":"IF(D5=\"additive\",\"ADDITIVE \", \"MULTIPLICATIVE \") & \"development\"","v":"ADDITIVE development"},null,null,null,null,null,"|"]
[null,null,"selected ultimate claims by AY (using paid claim development)",null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P7","v":2018},{"$f":"ROUND(IF($D$5=\"additive\",R7-Q7,R7/Q7),4)","v":4.4999999999999997E-3},{"$f":"ROUND(IF($D$5=\"additive\",S7-R7,S7/R7),4)","v":-3.3999999999999998E-3},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P8","v":2019},{"$f":"ROUND(IF($D$5=\"additive\",R8-Q8,R8/Q8),4)","v":1.6E-2},null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY","ult clms","  <===","sometimes you are not given the ultimate claims",null,null,null,null,null,null,null,"|",null,{"$f":"C13","v":2020},null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2017,34600,null,"  - you would then have to calculate them using an appropriate method",null,null,null,null,null,null,null,"|",null,"selected",{"$f":"ROUND(AVERAGE(Q14:Q16),4)","v":9.1000000000000004E-3},{"$f":"ROUND(AVERAGE(R14:R16),4)","v":-2E-3},{"$f":"ROUND(AVERAGE(S14:S16),4)","v":2.9999999999999997E-4},{"$f":"IF($D$5=\"additive\",0,1)","v":0},"  <===","tail = 1.0",null,null,null,null,null,"|"]
[null,null,2018,37715,null,"  - see 2016.Spring #23",null,null,null,null,null,null,null,"|",null,"cum",{"$f":"ROUND(IF($D$5=\"additive\",Q18+R19,Q18*R19),4)","v":7.4000000000000003E-3},{"$f":"ROUND(IF($D$5=\"additive\",R18+S19,R18*S19),4)","v":-1.6999999999999999E-3},{"$f":"ROUND(IF($D$5=\"additive\",S18+T19,S18*T19),4)","v":2.9999999999999997E-4},{"$f":"T18","v":0},"  <===","selected x (previous cum)",null,null,null,null,null,"|"]
[null,null,2019,36087,null,null,null,null,null,null,null,null,null,"|",null,"Ult Ratio",{"$f":"ROUND(IF($D$5=\"additive\",Q9+Q$19,Q9*Q$19),4)","v":2.8400000000000002E-2},{"$f":"ROUND(IF($D$5=\"additive\",R8+R$19,R8*R$19),4)","v":4.02E-2},{"$f":"ROUND(IF($D$5=\"additive\",S7+S$19,S7*S$19),4)","v":2.6499999999999999E-2},{"$f":"ROUND(IF($D$5=\"additive\",T6+T$19,T6*T$19),4)","v":3.5499999999999997E-2},"  <===","cum x (latest diagonal from Step 1)",null,null,null,null,null,"|"]
[null,null,2020,37990,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY",{"$f":"C21","v":2020},{"$f":"C20","v":2019},{"$f":"C19","v":2018},{"$f":"C18","v":2017},"  <===","given information",null,null,null,null,null,"|"]
[null,null,"When selecting development factors, you may select a SIMPLE AVERAGE in this problem.",null,null,null,null,null,null,null,null,null,null,"|",null,"ult clms",{"$f":"D21","v":37990},{"$f":"D20","v":36087},{"$f":"D19","v":37715},{"$f":"D18","v":34600},null,"(repeated here for convenience)",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"pd S/S",{"$f":"J13","v":153},{"$f":"K12","v":904},{"$f":"L11","v":887},{"$f":"M10","v":1229},null,null,null,null,null,null,null,"|"]
[null,null,"* There is no dvelopment beyond 48 months.",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 3:"," Ultimate S/S",null,"=","(Ultimate Ratio)",null,"x","(Ultimate Claims)",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null," Unpad S/S",null,"=","(Ultimate S/S)",null,"-","(Paid S/S)",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY","Ult S/S","UnPd S/S",null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C18","v":2017},{"$f":"IFERROR(T20*D18,\"n/a\")","v":1228.3},{"$f":"IFERROR(Q30-M10,\"n/a\")","v":-0.70000000000004547},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C19","v":2018},{"$f":"IFERROR(S20*D19,\"n/a\")","v":999.44749999999999},{"$f":"IFERROR(Q31-L11,\"n/a\")","v":112.44749999999999},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C20","v":2019},{"$f":"IFERROR(R20*D20,\"n/a\")","v":1450.6974},{"$f":"IFERROR(Q32-K12,\"n/a\")","v":546.69740000000002},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C13","v":2020},{"$f":"IFERROR(Q20*D21,\"--\")","v":1078.9160000000002},{"$f":"IFERROR(Q33-J13,\"--\")","v":925.91600000000017},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,{"$f":"SUM(Q30:Q33)","v":4757.3608999999997},{"$f":"SUM(R30:R33)","v":1584.3609000000001},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 4:",{"$f":"I5","v":"unpaid"},{"$f":"J5","v":"S/S"},{"$f":"K5","v":"for AY"},{"$f":"L5","v":2020},"=",{"$f":"VLOOKUP(S36,P32:R33,IF(P36=\"ultimate\",2,3),FALSE)","v":925.91600000000017},"  <===","final answer",null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","For COMPARISON, the S/S ultimate and unpaid values using standard paid S/S development are:",null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"Development method:",null,null,null,"% Difference: [ (ratio method) - (development method) ] / (ratio method)",null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY","Ult S/S","UnPd S/S",null,"Ult S/S","UnPd S/S",null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P30","v":2017},{"$f":"Y$98","v":1229},{"$f":"IFERROR(Q44-M10,\"n/a\")","v":0},null,{"$f":"IF(ABS(Q30)<0.1,\"-\",(Q30-Q44)/Q30)","v":-5.698933485305263E-4},1,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P31","v":2018},{"$f":"X98","v":995.5461187214612},{"$f":"IFERROR(Q45-L11,\"n/a\")","v":108.5461187214612},null,3.903537983274552E-3,3.4695135761477959E-2,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P32","v":2019},{"$f":"W98","v":1420.4363358228725},{"$f":"IFERROR(Q46-K12,\"n/a\")","v":516.43633582287248},null,2.085966665214092E-2,5.5352493311889787E-2,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P33","v":2020},{"$f":"V98","v":992.95810931671144},{"$f":"IFERROR(Q47-J13,\"--\")","v":839.95810931671144},null,7.9670605203082265E-2,9.2835517134695483E-2,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,{"$f":"SUM(Q44:Q47)","v":4637.9405638610451},{"$f":"SUM(R44:R47)","v":1464.9405638610451},null,2.5102223406879759E-2,7.5374452966464264E-2,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["2016.Fall #24(b)",null,"Use the","multiplicative",null,"ratio method to estimate the",null,null,"ultimate","S/S","for AY",2014,null,"|","SIDE calculation for ultimate claims:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"cumulative paid claims:",null,null,null,null,null,"cumulative paid SS:",null,null,null,null,"|",null,"pd clm ratios:",null,null,null,null,null,"SS ratios"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY",12,24,36,48,null,"AY",12,24,36,48,"|","AY",{"$f":"D66&\"-\"&E66","v":"12-24"},{"$f":"E66&\"-\"&F66","v":"24-36"},{"$f":"F66&\"-\"&G66","v":"36-48"},null,null,"AY",{"$f":"P66","v":"12-24"},{"$f":"Q66","v":"24-36"},{"$f":"R66","v":"36-48"}]
[null,null,{"$f":"C68-1","v":2011},200,560,570,570,null,{"$f":"I68-1","v":2011},20,90,100,100,"|",{"$f":"C67","v":2011},{"$f":"E67/D67","v":2.8},{"$f":"F67/E67","v":1.0178571428571428},{"$f":"G67/F67","v":1},null,null,{"$f":"C67","v":2011},{"$f":"K67/J67","v":4.5},{"$f":"L67/K67","v":1.1111111111111112},{"$f":"M67/L67","v":1}]
[null,null,{"$f":"C69-1","v":2012},150,250,400,null,null,{"$f":"I69-1","v":2012},16,40,70,null,"|",{"$f":"C68","v":2012},{"$f":"E68/D68","v":1.6666666666666667},{"$f":"F68/E68","v":1.6},null,null,null,{"$f":"C68","v":2012},{"$f":"K68/J68","v":2.5},{"$f":"L68/K68","v":1.75}]
[null,null,{"$f":"C70-1","v":2013},150,350,null,null,null,{"$f":"I70-1","v":2013},15,56,null,null,"|",{"$f":"C69","v":2013},{"$f":"E69/D69","v":2.3333333333333335},null,null,null,null,{"$f":"C69","v":2013},{"$f":"K69/J69","v":3.7333333333333334},{"$f":"L69/K69","v":0}]
[null,null,2014,50,null,null,null,null,{"$f":"C70","v":2014},5,null,null,null,"|",{"$f":"C70","v":2014},null,null,null,null,null,{"$f":"C70","v":2014}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"selected ultimate claims by AY (using paid claim development)",null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY","ult clms",null,null,null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C76-1","v":2011},{"$f":"ROUND(G67,0)","v":570},"<==","paid claims development method",null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C77-1","v":2012},{"$f":"ROUND(F68*R$96,0)","v":445},"<==","paid claims development method",null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C78-1","v":2013},{"$f":"ROUND(E69*Q$96,0)","v":585},"<==","paid claims development method",null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C70","v":2014},150,"<==","given in the statement of the exam problem",null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"When selecting development factors, you may select a SIMPLE AVERAGE in this problem.",null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Random",null,"Use the","multiplicative",null,"approach to estimate the",null,null,{"$f":"IF(RAND()<0.5,\"unpaid\",\"ultimate\")","v":"ultimate"},"S/S","for AY",{"$f":"C99","v":2020},null,"|","The actual LDFs that are used are randomized values around the values in red."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"cumulative paid claims:",null,null,null,null,null,"cumulative paid SS:",null,null,null,null,"|","LDF basis (paid claims)",null,null,null,null,null,"LDF basis (paid S/S)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY",12,24,36,48,null,"AY",12,24,36,48,"|","AY","12-24","24-36","36-48","48-",null,"AY","12-24","24-36","36-48","48-"]
[null,null,{"$f":"C89-1","v":2017},{"$f":"RANDBETWEEN(30,80)*100","v":7200},{"$f":"ROUND(D88*$P$88*RANDBETWEEN(90,110)/100,-2)","v":23500},{"$f":"ROUND(E88*$Q$88*RANDBETWEEN(95,105)/100,-2)","v":34900},{"$f":"ROUND(F88*$R$88*RANDBETWEEN(98,102)/100,-2)","v":38800},null,{"$f":"C88","v":2017},{"$f":"ROUND(D88*RANDBETWEEN(20,30)/1000,0)","v":202},{"$f":"ROUND(J88*$V$88*RANDBETWEEN(80,120)/100,0)","v":814},{"$f":"ROUND(K88*$W$88*RANDBETWEEN(80,110)/100,0)","v":1185},{"$f":"ROUND(L88*$X$88*RANDBETWEEN(100,105)/100,0)","v":1356},"|","AY",3,1.5,1.1000000000000001,1,null,"AY",4.2,1.6,1.1000000000000001,1]
[null,null,{"$f":"C90-1","v":2018},{"$f":"ROUND(D88*RANDBETWEEN(80,120)/100,-2)","v":6800},{"$f":"ROUND(D89*$P$88*RANDBETWEEN(90,110)/100,-2)","v":18400},{"$f":"ROUND(E89*$Q$88*RANDBETWEEN(95,105)/100,-2)","v":27600},null,null,{"$f":"C89","v":2018},{"$f":"ROUND(D89*RANDBETWEEN(20,30)/1000,0)","v":136},{"$f":"ROUND(J89*$V$88*RANDBETWEEN(80,120)/100,0)","v":668},{"$f":"ROUND(K89*$W$88*RANDBETWEEN(80,110)/100,0)","v":962},null,"|"]
[null,null,{"$f":"C91-1","v":2019},{"$f":"ROUND(D88*RANDBETWEEN(80,120)/100,-2)","v":8100},{"$f":"ROUND(D90*$P$88*RANDBETWEEN(90,110)/100,-2)","v":24100},null,null,null,{"$f":"C90","v":2019},{"$f":"ROUND(D90*RANDBETWEEN(20,30)/1000,0)","v":211},{"$f":"ROUND(J90*$V$88*RANDBETWEEN(80,120)/100,0)","v":1001},null,null,"|"]
[null,null,{"$f":"RANDBETWEEN(2019,2021)","v":2020},{"$f":"ROUND(D88*RANDBETWEEN(80,120)/100,-2)","v":6600},null,null,null,null,{"$f":"C91","v":2020},{"$f":"ROUND(D91*RANDBETWEEN(20,30)/1000,0)","v":185},null,null,null,"|",null,"below are the actual PAID CLAIMS LDFs",null,null,null,null,null,"below are the actual S/S LDFs"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","check",{"$f":"E10/D10","v":3.3030303030303032},{"$f":"F10/E10","v":1.426605504587156},{"$f":"G10/F10","v":1.112540192926045},null,null,"check",{"$f":"K10/J10","v":4.0732984293193715},{"$f":"L10/K10","v":1.4074550128534704},{"$f":"M10/L10","v":1.1223744292237443}]
[null,null,"selected ultimate claims by AY (using paid claim development)",null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"E11/D11","v":3.3076923076923075},{"$f":"F11/E11","v":1.5767441860465117},null,null,null,null,{"$f":"K11/J11","v":3.9079754601226995},{"$f":"L11/K11","v":1.3924646781789638}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"E12/D12","v":2.7341772151898733},null,null,null,null,null,{"$f":"K12/J12","v":4.409756097560976}]
[null,null,"AY","ult clms","  <===","sometimes you are not given the ultimate claims",null,null,null,null,null,null,null,"|","avg",{"$f":"AVERAGE(P92:P94)","v":3.114966608637495},{"$f":"AVERAGE(Q92:Q94)","v":1.5016748453168338},{"$f":"AVERAGE(R92:R94)","v":1.112540192926045},1,null,"avg",{"$f":"AVERAGE(V92:V94)","v":4.1303433290010156},{"$f":"AVERAGE(W92:W94)","v":1.399959845516217},{"$f":"AVERAGE(X92:X94)","v":1.1223744292237443},1]
[null,null,{"$f":"C88","v":2017},{"$f":"ROUND(G88,0)","v":38800},null,"  - you would then have to calculate them using an appropriate method",null,null,null,null,null,null,null,"|","cum",{"$f":"P95*Q96","v":5.2040925468383055},{"$f":"Q95*R96","v":1.670673622120979},{"$f":"R95*S96","v":1.112540192926045},{"$f":"S95","v":1},null,"cum",{"$f":"V95*W96","v":6.489922283115761},{"$f":"W95*X96","v":1.5712791325474254},{"$f":"X95*Y96","v":1.1223744292237443},{"$f":"Y95","v":1}]
[null,null,{"$f":"C89","v":2018},{"$f":"ROUND(F89*R$96,0)","v":30706},null,"  - see 2016.Spring #23",null,null,null,null,null,null,null,"|","LD",{"$f":"D13","v":7300},{"$f":"E12","v":21600},{"$f":"F11","v":33900},{"$f":"G10","v":34600},null,"LD",{"$f":"J13","v":153},{"$f":"K12","v":904},{"$f":"L11","v":887},{"$f":"M10","v":1229}]
[null,null,{"$f":"C90","v":2019},{"$f":"ROUND(E90*Q$96,0)","v":40263},null,null,null,null,null,null,null,null,null,"|","ult",{"$f":"P97*P96","v":37989.875591919626},{"$f":"Q97*Q96","v":36086.55023781315},{"$f":"R97*R96","v":37715.112540192924},{"$f":"S97*S96","v":34600},null,"ult",{"$f":"V97*V96","v":992.95810931671144},{"$f":"W97*W96","v":1420.4363358228725},{"$f":"X97*X96","v":995.5461187214612},{"$f":"Y97*Y96","v":1229}]
[null,null,{"$f":"C91","v":2020},{"$f":"ROUND(D91*$P$96,0)","v":34347},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","* The check only works if the problem at the top was randomly generated."]
[null,null,"When selecting development factors, you may select a SIMPLE AVERAGE in this problem.",null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]

{"sheet":"2","index":2,"n_rows":119,"n_cols":28,"rows_kept":119,"cut":false,"hidden":false,"merged":[]}
["Reading:",null,"Friedland 14 (Reinsurance)",null,null,null,null,null,null,null,null,null,"Return to TOC","|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Model:",null,"2017.Fall #25",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem Type:",null,"Apply reinsurance treaties and calculate net unpaid claims",null,null,null,null,null,null,null,null,null,null,"|","Step 1:","Calculate the net reported claims triangle as (gross reported) - (ceded reported)",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem",null,"Calculate the net unpaid claims for all accident years using reported claims development.",null,null,null,null,null,null,null,null,null,null,"|",null,"AY",12,24,36,48,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P7-1","v":2013},{"$f":"D10-J10","v":3600},{"$f":"E10-K10","v":6894},{"$f":"F10-L10","v":8142},{"$f":"G10-M10","v":8370},null,null,null,null,null,null,null,"|"]
[null,null,"cumulative gross reported claims:",null,null,null,null,null,"cumulative ceded reported claims:",null,null,null,null,"|",null,{"$f":"P8-1","v":2014},{"$f":"D11-J11","v":3230},{"$f":"E11-K11","v":6185},{"$f":"F11-L11","v":7304},null,null,null,null,null,null,null,null,"|"]
[null,null,"(no reported claim development beyond 48 months)",null,null,null,null,null,"(under excess-of-loss treaty)",null,null,null,null,"|",null,{"$f":"P9-1","v":2015},{"$f":"D12-J12","v":8470},{"$f":"E12-K12","v":16220},null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY",12,24,36,48,null,"AY",12,24,36,48,"|",null,{"$f":"C13","v":2016},{"$f":"D13-J13","v":5830},null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2013,3600,7214,9852,10300,null,2013,0,320,1710,1930,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2014,3400,6355,8674,null,null,2014,170,170,1370,null,"|","Step 2:","Calculate net ultimate claims using reported development on the net triangle above (net of excess-of-loss)",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2015,8600,16350,null,null,null,2015,130,130,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2016,6000,null,null,null,null,2016,170,null,null,null,"|",null,"AY",{"$f":"Q5&\"-\"&R5","v":"12-24"},{"$f":"R5&\"-\"&S5","v":"24-36"},{"$f":"S5&\"-\"&T5","v":"36-48"},{"$f":"T5&\"-\"&H9","v":"48-"},null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P6","v":2013},{"$f":"ROUND(IF($D$5=\"additive\",R6-Q6,R6/Q6),4)","v":1.915},{"$f":"ROUND(IF($D$5=\"additive\",S6-R6,S6/R6),4)","v":1.181},{"$f":"ROUND(IF($D$5=\"additive\",T6-S6,T6/S6),4)","v":1.028},null,"  <===",{"$f":"IF(D5=\"additive\",\"ADDITIVE \", \"MULTIPLICATIVE \") & \"development\"","v":"MULTIPLICATIVE development"},null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P7","v":2014},{"$f":"ROUND(IF($D$5=\"additive\",R7-Q7,R7/Q7),4)","v":1.9149},{"$f":"ROUND(IF($D$5=\"additive\",S7-R7,S7/R7),4)","v":1.1809000000000001},null,null,null,null,null,null,null,null,null,"|"]
[null,null,"cumulative net paid claims:",null,null,null,null,null,"stop-loss limits",null,null,null,null,"|",null,{"$f":"P8","v":2015},{"$f":"ROUND(IF($D$5=\"additive\",R8-Q8,R8/Q8),4)","v":1.915},null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"(net of excess-of-loss treaty)",null,null,null,null,null,"(applies AFTER excess-of-loss treaty)",null,null,null,null,"|",null,{"$f":"C13","v":2016},null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY","pd clm",null,null,null,null,"AY","limit",null,null,null,"|",null,"selected",{"$f":"ROUND(AVERAGE(Q14:Q16),4)","v":1.915},{"$f":"ROUND(AVERAGE(R14:R16),4)","v":1.181},{"$f":"ROUND(AVERAGE(S14:S16),4)","v":1.028},{"$f":"IF($D$5=\"additive\",0,1)","v":1},"  <===","tail = 1.0",null,null,null,null,null,"|"]
[null,null,2013,8200,null,null,null,null,2013,10000,null,null,null,"|",null,"cum",{"$f":"ROUND(IF($D$5=\"additive\",Q18+R19,Q18*R19),4)","v":2.3250000000000002},{"$f":"ROUND(IF($D$5=\"additive\",R18+S19,R18*S19),4)","v":1.2141},{"$f":"ROUND(IF($D$5=\"additive\",S18+T19,S18*T19),4)","v":1.028},{"$f":"T18","v":1},"  <===","selected x (previous cum)",null,null,null,null,null,"|"]
[null,null,2014,6100,null,null,null,null,2014,10000,null,null,null,"|",null,"Ult Clms",{"$f":"ROUND(IF($D$5=\"additive\",Q9+Q$19,Q9*Q$19),0)","v":13555},{"$f":"ROUND(IF($D$5=\"additive\",R8+R$19,R8*R$19),0)","v":19693},{"$f":"ROUND(IF($D$5=\"additive\",S7+S$19,S7*S$19),0)","v":7509},{"$f":"ROUND(IF($D$5=\"additive\",T6+T$19,T6*T$19),0)","v":8370},"  <===","cum x (latest diagonal from Step 1)",null,null,null,null,null,"|"]
[null,null,2015,9000,null,null,null,null,2015,12000,null,null,null,"|",null,"net of EoL",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2016,2400,null,null,null,null,2016,9500,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 3:","Put the results from Step 2 into a table and apply the given stop-loss limits",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"There is no further loss development past 48 months",null,null,null,null,null,null,null,null,null,null,"|",null,null,"Ult Clms","stop-loss","Ult Clms","net","net",null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY","net of EoL","limit","net of ALL","paid","unpaid",null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P6","v":2013},{"$f":"T20","v":8370},{"$f":"J19","v":10000},{"$f":"MIN(Q27,R27)","v":8370},{"$f":"D19","v":8200},{"$f":"MAX(0,S27-T27)","v":170},"  <===","final answer",null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P7","v":2014},{"$f":"S20","v":7509},{"$f":"J20","v":10000},{"$f":"MIN(Q28,R28)","v":7509},{"$f":"D20","v":6100},{"$f":"MAX(0,S28-T28)","v":1409},"  <===","final answer",null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P8","v":2015},{"$f":"R20","v":19693},{"$f":"J21","v":12000},{"$f":"MIN(Q29,R29)","v":12000},{"$f":"D21","v":9000},{"$f":"MAX(0,S29-T29)","v":3000},"  <===","final answer",null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P9","v":2016},{"$f":"Q20","v":13555},{"$f":"J22","v":9500},{"$f":"MIN(Q30,R30)","v":9500},{"$f":"D22","v":2400},{"$f":"MAX(0,S30-T30)","v":7100},"  <===","final answer",null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"TOTAL",null,null,null,null,{"$f":"SUM(U27:U30)","v":11679},null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Model","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----"]
["Reading:",null,"Friedland 14 (Reinsurance)",null,null,null,null,null,null,null,null,null,null,"|"]
["Model:",null,"2017.Fall #25",null,null,null,null,null,null,null,null,null,null,"|"]
["Problem Type:",null,"Apply reinsurance treaties and calculate net unpaid claims",null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem",null,"Calculate the net unpaid claims for all accident years using reported claims development.",null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"cumulative gross reported claims:",null,null,null,null,null,"cumulative ceded reported claims:",null,null,null,null,"|",null,"net LDFs (from solution)",null,null,null,null,null,"randomized LDFs"]
[null,null,"(no reported claim development beyond 48 months)",null,null,null,null,null,"(under excess-of-loss treaty)",null,null,null,null,"|"]
[null,null,"AY",12,24,36,48,null,"AY",12,24,36,48,"|",null,"AY",null,null,null,null,null,"AY"]
[null,null,{"$f":"C71-1","v":2013},2757,5570,6880,7047,null,{"$f":"C70","v":2013},0,745,1332,1332,"|",null,{"$f":"P71-1","v":2013},{"$f":"Q14","v":1.915},{"$f":"R14","v":1.181},{"$f":"S14","v":1.028},null,null,{"$f":"V71-1","v":2013},{"$f":"RANDBETWEEN(1500,2000)/1000","v":1.56},{"$f":"RANDBETWEEN(1100,1200)/1000","v":1.103},{"$f":"RANDBETWEEN(1010,1050)/1000","v":1.0409999999999999}]
[null,null,{"$f":"C72-1","v":2014},2345,4104,5121,null,null,{"$f":"C71","v":2014},0,0,402,null,"|",null,{"$f":"P72-1","v":2014},{"$f":"Q15","v":1.9149},{"$f":"R15","v":1.1809000000000001},null,null,null,{"$f":"V72-1","v":2014},{"$f":"W70","v":1.56},{"$f":"X70","v":1.103}]
[null,null,{"$f":"C73-1","v":2015},2639,4677,null,null,null,{"$f":"C72","v":2015},154,328,null,null,"|",null,{"$f":"P73-1","v":2015},{"$f":"Q16","v":1.915},null,null,null,null,{"$f":"V73-1","v":2015},{"$f":"W70","v":1.56}]
[null,null,2016,2802,null,null,null,null,{"$f":"C73","v":2016},0,null,null,null,"|",null,2016,null,null,null,null,null,2016]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"cumulative net paid claims:",null,null,null,null,null,"stop-loss limits",null,null,null,null,"|",null,"back into gross reported (except age 12)",null,null,null,null,null,"randomized ceded"]
[null,null,"(net of excess-of-loss treaty)",null,null,null,null,null,"(applies AFTER excess-of-loss treaty)",null,null,null,null,"|"]
[null,null,"AY","pd clm",null,null,null,null,"AY","limit",null,null,null,"|",null,"AY",null,null,null,null,null,"AY",12,24,36,48]
[null,null,{"$f":"C70","v":2013},5102,null,null,null,null,{"$f":"C70","v":2013},5000,null,null,null,"|",null,{"$f":"P80-1","v":2013},{"$f":"RANDBETWEEN(20,90)*100","v":8600},{"$f":"ROUND((Q79-W79)*W70+X79,0)","v":13416},{"$f":"ROUND((R79-X79)*X70+Y79,0)","v":16308},{"$f":"ROUND((S79-Y79)*Y70+Z79,-2)","v":16900},null,{"$f":"I70","v":2013},{"$f":"IF(RAND()<0.5,0,RANDBETWEEN(10,20)*10)","v":0},{"$f":"W79+IF(RAND()<0.5,0,RANDBETWEEN(30,100)*10)","v":0},{"$f":"X79+IF(RAND()<0.5,0,RANDBETWEEN(100,175)*10)","v":1510},{"$f":"Y79+IF(RAND()<0.5,0,RANDBETWEEN(20,55)*10)","v":1510}]
[null,null,{"$f":"C71","v":2014},3834,null,null,null,null,{"$f":"C71","v":2014},5000,null,null,null,"|",null,{"$f":"P81-1","v":2014},{"$f":"RANDBETWEEN(20,90)*100","v":2200},{"$f":"ROUND((Q80-W80)*W71+X80,0)","v":3788},{"$f":"ROUND((R80-X80)*X71+Y80,0)","v":4117},null,null,{"$f":"I71","v":2014},{"$f":"IF(RAND()<0.5,0,RANDBETWEEN(10,20)*10)","v":150},{"$f":"W80+IF(RAND()<0.5,0,RANDBETWEEN(30,100)*10)","v":590},{"$f":"X80+IF(RAND()<0.5,0,RANDBETWEEN(100,175)*10)","v":590}]
[null,null,{"$f":"C72","v":2015},2840,null,null,null,null,{"$f":"C72","v":2015},5000,null,null,null,"|",null,{"$f":"P82-1","v":2015},{"$f":"RANDBETWEEN(20,90)*100","v":2200},{"$f":"ROUND((Q81-W81)*W72+X81,0)","v":4112},null,null,null,{"$f":"I72","v":2015},{"$f":"IF(RAND()<0.5,0,RANDBETWEEN(10,20)*10)","v":160},{"$f":"W81+IF(RAND()<0.5,0,RANDBETWEEN(30,100)*10)","v":930}]
[null,null,{"$f":"C73","v":2016},1385,null,null,null,null,{"$f":"C73","v":2016},"none",null,null,null,"|",null,2016,{"$f":"RANDBETWEEN(20,90)*100","v":2300},null,null,null,null,{"$f":"I73","v":2016},{"$f":"IF(RAND()<0.5,0,RANDBETWEEN(10,20)*10)","v":100}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"calc net LDFs",{"$f":"(R79-X79)/(Q79-W79)","v":1.56},{"$f":"(S79-Y79)/(R79-X79)","v":1.1030113297555157},{"$f":"(T79-Z79)/(S79-Y79)","v":1.0400054061359643}]
[null,null,"There is no further loss development past 48 months",null,null,null,null,null,null,null,null,null,null,"|",null,null,{"$f":"(R80-X80)/(Q80-W80)","v":1.56},{"$f":"(S80-Y80)/(R80-X80)","v":1.1028767979987493}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,{"$f":"(R81-X81)/(Q81-W81)","v":1.5598039215686275}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"* should match randomized LDFs"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"check:",{"$f":"Q84-W70","v":0},1.1329755515765427E-5,-9.9459386403566441E-4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,0,-1.2320200125071068E-4,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,{"$f":"Q86-W72","v":-1.9607843137259273E-4}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"randomized paid loss",null,null,null,null,null,"randomized stop-loss"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY","pd clm",null,null,null,null,"AY","limit"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C79","v":2013},{"$f":"ROUND(T79*R104,-2)","v":13500},null,null,null,null,{"$f":"P96","v":2013},{"$f":"IF(RAND()<0.25,\"none\",RANDBETWEEN(16,24)*500)","v":"none"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C80","v":2014},{"$f":"ROUND(S80*R105,-2)","v":2900},null,null,null,null,{"$f":"P97","v":2014},{"$f":"IF(RAND()<0.25,\"none\",RANDBETWEEN(16,24)*500)","v":11500}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C81","v":2015},{"$f":"ROUND(R81*R106,-2)","v":2300},null,null,null,null,{"$f":"P98","v":2015},{"$f":"IF(RAND()<0.25,\"none\",RANDBETWEEN(16,24)*500)","v":10000}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C82","v":2016},{"$f":"ROUND(Q82*R107,-2)","v":900},null,null,null,null,{"$f":"P99","v":2016},{"$f":"IF(RAND()<0.25,\"none\",RANDBETWEEN(16,24)*500)","v":10500}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"given ratios for paid"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY","ratio","selected"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P105-1","v":2013},{"$f":"D79/G70","v":0.72399602667801899},0.8]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P106-1","v":2014},{"$f":"D80/F71","v":0.74868189806678387},0.7]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P107-1","v":2015},{"$f":"D81/E72","v":0.60722685482146677},0.55000000000000004]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,2016,{"$f":"D82/D73","v":0.49428979300499643},0.4]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]

{"sheet":"3","index":3,"n_rows":119,"n_cols":39,"rows_kept":119,"cut":false,"hidden":false,"merged":[[22,31,22,32],[22,33,22,34],[22,35,22,36],[22,37,22,38],[22,29,22,30]]}
["Reading:",null,"Friedland 16 (ALAE)",null,null,null,null,null,null,null,null,null,"Return to TOC","|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Model:",null,"2019.Spring #24",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem Type:",null,"Additive or Multiplicative approach for ALAE",null,null,null,null,null,null,null,null,null,null,"|","Step 1:","Ratio of cumulative paid ALAE to cumulative paid claims:",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem",null,"Use the","additive",null,"approach to estimate the",null,null,"unpaid","ALAE","for AY",2020,null,"|",null,"AY",12,24,36,48,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P7-1","v":2017},{"$f":"ROUND(J10/D10,4)","v":2.5899999999999999E-2},{"$f":"ROUND(K10/E10,4)","v":3.4599999999999999E-2},{"$f":"ROUND(L10/F10,4)","v":3.6600000000000001E-2},{"$f":"ROUND(M10/G10,4)","v":3.5900000000000001E-2},null,null,null,null,null,null,null,"|"]
[null,null,"cumulative paid claims:",null,null,null,null,null,"cumulative paid ALAE:",null,null,null,null,"|",null,{"$f":"P8-1","v":2018},{"$f":"ROUND(J11/D11,4)","v":2.9000000000000001E-2},{"$f":"ROUND(K11/E11,4)","v":4.0500000000000001E-2},{"$f":"ROUND(L11/F11,4)","v":4.1099999999999998E-2},null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P9-1","v":2019},{"$f":"ROUND(J12/D12,4)","v":2.1999999999999999E-2},{"$f":"ROUND(K12/E12,4)","v":2.9700000000000001E-2},null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY",12,24,36,48,null,"AY",12,24,36,48,"|",null,{"$f":"C13","v":2020},{"$f":"ROUND(J13/D13,4)","v":0.02},null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2017,5900,19500,30400,33400,null,2017,153,675,1112,1199,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2018,6700,19500,29800,null,null,2018,194,790,1226,null,"|","Step 2:","Development triangle (either additive or multiplicative as appropriate):",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2019,5900,17300,null,null,null,2019,130,513,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2020,5800,null,null,null,null,2020,116,null,null,null,"|",null,"AY",{"$f":"Q5&\"-\"&R5","v":"12-24"},{"$f":"R5&\"-\"&S5","v":"24-36"},{"$f":"S5&\"-\"&T5","v":"36-48"},{"$f":"T5&\"-\"&H9","v":"48-"},null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P6","v":2017},{"$f":"ROUND(IF($D$5=\"additive\",R6-Q6,R6/Q6),4)","v":8.6999999999999994E-3},{"$f":"ROUND(IF($D$5=\"additive\",S6-R6,S6/R6),4)","v":2E-3},{"$f":"ROUND(IF($D$5=\"additive\",T6-S6,T6/S6),4)","v":-6.9999999999999999E-4},null,"  <===",{"$f":"IF(D5=\"additive\",\"ADDITIVE \", \"MULTIPLICATIVE \") & \"development\"","v":"ADDITIVE development"},null,null,null,null,null,"|"]
[null,null,"selected ultimate claims by AY",null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P7","v":2018},{"$f":"ROUND(IF($D$5=\"additive\",R7-Q7,R7/Q7),4)","v":1.15E-2},{"$f":"ROUND(IF($D$5=\"additive\",S7-R7,S7/R7),4)","v":5.9999999999999995E-4},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"P8","v":2019},{"$f":"ROUND(IF($D$5=\"additive\",R8-Q8,R8/Q8),4)","v":7.7000000000000002E-3},null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY","ult clms","  <===","sometimes you are not given the ultimate claims",null,null,null,null,null,null,null,"|",null,{"$f":"C13","v":2020},null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2017,33400,null,"  - you would then have to calculate them using an appropriate method",null,null,null,null,null,null,null,"|",null,"selected",{"$f":"ROUND(AVERAGE(Q14:Q16),4)","v":9.2999999999999992E-3},{"$f":"ROUND(AVERAGE(R14:R16),4)","v":1.2999999999999999E-3},{"$f":"ROUND(AVERAGE(S14:S16),4)","v":-6.9999999999999999E-4},{"$f":"IF($D$5=\"additive\",0,1)","v":0},"  <===","tail = 0.0 if additive OR 1.0 if multiplicative",null,null,null,null,null,"|"]
[null,null,2018,33087,null,"  - see 2016.Spring #23",null,null,null,null,null,null,null,"|",null,"cum",{"$f":"ROUND(IF($D$5=\"additive\",Q18+R19,Q18*R19),4)","v":9.9000000000000008E-3},{"$f":"ROUND(IF($D$5=\"additive\",R18+S19,R18*S19),4)","v":5.9999999999999995E-4},{"$f":"ROUND(IF($D$5=\"additive\",S18+T19,S18*T19),4)","v":-6.9999999999999999E-4},{"$f":"T18","v":0},"  <===",{"$f":"IF(D5=\"additive\",\"ADDITIVE:  selected + (previous cum)\", \"MULTIPLICATIVE:  selected x (previous cum)\")","v":"ADDITIVE:  selected + (previous cum)"},null,null,null,null,null,"|"]
[null,null,2019,29413,null,null,null,null,null,null,null,null,null,"|",null,"Ult Ratio",{"$f":"ROUND(IF($D$5=\"additive\",Q9+Q$19,Q9*Q$19),4)","v":2.9899999999999999E-2},{"$f":"ROUND(IF($D$5=\"additive\",R8+R$19,R8*R$19),4)","v":3.0300000000000001E-2},{"$f":"ROUND(IF($D$5=\"additive\",S7+S$19,S7*S$19),4)","v":4.0399999999999998E-2},{"$f":"ROUND(IF($D$5=\"additive\",T6+T$19,T6*T$19),4)","v":3.5900000000000001E-2},"  <===",{"$f":"IF(D5=\"additive\",\"ADDITIVE:  cum + (latest diagonal from Step 1)\",\"MULTIPLICATIVE:  cum x (latest diagonal from Step 1)\")","v":"ADDITIVE:  cum + (latest diagonal from Step 1)"},null,null,null,null,null,"|"]
[null,null,2020,30549,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY",{"$f":"C21","v":2020},{"$f":"C20","v":2019},{"$f":"C19","v":2018},{"$f":"C18","v":2017},"  <===","given information",null,null,null,null,null,"|",null,"parameters for 2-point exponential fit:   y = aebx"]
[null,null,"When selecting development factors, you may select a SIMPLE AVERAGE in this problem.",null,null,null,null,null,null,null,null,null,null,"|",null,"ult clms",{"$f":"D21","v":30549},{"$f":"D20","v":29413},{"$f":"D19","v":33087},{"$f":"D18","v":33400},null,"(repeated here for convenience)",null,null,null,null,null,"|",null,"0 - 12",null,"12 - 24",null,"24 - 36",null,"36 - 48",null,"48 - 60"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"pd ALAE",{"$f":"J13","v":116},{"$f":"K12","v":513},{"$f":"L11","v":1226},{"$f":"M10","v":1199},null,null,null,null,null,null,null,"|","AY","1 + b","a","1 + b","a","1 + b","a","1 + b","a","1 + b","a"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|",2022,"use 12 - 24 values",null,{"$f":"LOGEST(D17:E17,D10:E10,1,1)","v":{"$error":"#VALUE!"}},{"$error":"#VALUE!"},{"$f":"LOGEST(E17:F17,E10:F10,1,1)","v":{"$error":"#VALUE!"}},{"$error":"#VALUE!"},{"$f":"LOGEST(F17:G17,F10:G10,1,1)","v":{"$error":"#VALUE!"}},{"$error":"#VALUE!"},"not needed"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 3:"," Ultimate ALAE",null,"=","(Ultimate Ratio)",null,"x","(Ultimate Claims)",null,null,null,null,null,"|",{"$f":"AC25+1","v":2023},"use 12 - 24 values",null,{"$f":"LOGEST(D18:E18,D11:E11,1,1)","v":{"$error":"#VALUE!"}},{"$error":"#VALUE!"},{"$f":"LOGEST(E18:F18,E11:F11,1,1)","v":{"$error":"#VALUE!"}},{"$error":"#VALUE!"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null," Unpad ALAE",null,"=","(Ultimate ALAE)",null,"-","(Paid ALAE)",null,null,null,null,null,"|",{"$f":"AC26+1","v":2024},"use 12 - 24 values",null,{"$f":"LOGEST(D19:E19,D12:E12,1,1)","v":{"$error":"#VALUE!"}},{"$error":"#VALUE!"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|",{"$f":"AC27+1","v":2025},"use 12 - 24 values"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"AY","Ult ALAE","UnPd ALAE",null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C18","v":2017},{"$f":"T20*D18","v":1199.06},{"$f":"Q30-M10","v":5.999999999994543E-2},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C19","v":2018},{"$f":"S20*D19","v":1336.7148},{"$f":"Q31-L11","v":110.71479999999997},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C20","v":2019},{"$f":"R20*D20","v":891.21389999999997},{"$f":"Q32-K12","v":378.21389999999997},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"C13","v":2020},{"$f":"Q20*D21","v":913.41509999999994},{"$f":"Q33-J13","v":797.41509999999994},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,{"$f":"SUM(Q30:Q33)","v":4340.4038},{"$f":"SUM(R30:R33)","v":1286.4037999999998},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 4:",{"$f":"I5","v":"unpaid"},{"$f":"J5","v":"ALAE"},{"$f":"K5","v":"for AY"},{"$f":"L5","v":2020},"=",{"$f":"VLOOKUP(S36,P32:R33,IF(P36=\"ultimate\",2,3),FALSE)","v":797.41509999999994},"  <===","final answer",null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["2019.Spring #24",null,"Use the","multiplicative",null,"approach to estimate the",null,null,"ultimate","ALAE","for AY",2018,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"cumulative paid claims:",null,null,null,null,null,"cumulative paid ALAE:",null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY",12,24,36,48,null,"AY",12,24,36,48,"|"]
[null,null,{"$f":"C68-1","v":2015},3800,10640,15960,17556,null,{"$f":"I68-1","v":2015},77,316,512,571,"|",null,{"$f":"E67/D67","v":2.8},{"$f":"F67/E67","v":1.5},{"$f":"G67/F67","v":1.1000000000000001},null,null,null,{"$f":"K67/J67","v":4.1038961038961039},{"$f":"L67/K67","v":1.620253164556962},{"$f":"M67/L67","v":1.115234375}]
[null,null,{"$f":"C69-1","v":2016},3900,10920,15600,null,null,{"$f":"I69-1","v":2016},81,337,517,null,"|",null,{"$f":"E68/D68","v":2.8},{"$f":"F68/E68","v":1.4285714285714286},null,null,null,null,{"$f":"K68/J68","v":4.1604938271604937},{"$f":"L68/K68","v":1.5341246290801187}]
[null,null,{"$f":"C70-1","v":2017},3850,11858,null,null,null,{"$f":"I70-1","v":2017},75,334,null,null,"|",null,{"$f":"E69/D69","v":3.08},null,null,null,null,null,{"$f":"K69/J69","v":4.4533333333333331},{"$f":"L69/K69","v":0}]
[null,null,2018,4050,null,null,null,null,{"$f":"C70","v":2018},82,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"selected ultimate claims by AY",null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY","ult clms","  <===","sometimes you are not given the ultimate claims",null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C76-1","v":2015},17500,null,"  - you would then have to calculate them using an appropriate method",null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C77-1","v":2016},17900,null,"  - see 2016.Spring #23",null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C78-1","v":2017},17600,null,null,null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C70","v":2018},18500,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"When selecting development factors, you may select a SIMPLE AVERAGE in this problem.",null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Random",null,"Use the",{"$f":"IF(RAND()<0.5,\"additive\",\"multiplicative\")","v":"additive"},null,"approach to estimate the",null,null,{"$f":"IF(RAND()<0.5,\"unpaid\",\"ultimate\")","v":"ultimate"},"ALAE","for AY",{"$f":"C99","v":2019},null,"|","The actual LDFs that are used are randomized values around the values in red."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"cumulative paid claims:",null,null,null,null,null,"cumulative paid ALAE:",null,null,null,null,"|","LDF basis (paid claims)",null,null,null,null,null,"LDF basis (paid ALAE)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"AY",12,24,36,48,null,"AY",12,24,36,48,"|","AY","12-24","24-36","36-48","48-",null,"AY","12-24","24-36","36-48","48-"]
[null,null,{"$f":"C89-1","v":2016},{"$f":"RANDBETWEEN(30,80)*100","v":5000},{"$f":"ROUND(D88*$P$88*RANDBETWEEN(90,110)/100,-2)","v":15000},{"$f":"ROUND(E88*$Q$88*RANDBETWEEN(95,105)/100,-2)","v":21600},{"$f":"ROUND(F88*$R$88*RANDBETWEEN(98,102)/100,-2)","v":23300},null,{"$f":"C88","v":2016},{"$f":"ROUND(D88*RANDBETWEEN(20,30)/1000,0)","v":100},{"$f":"ROUND(J88*$V$88*RANDBETWEEN(90,110)/100,0)","v":378},{"$f":"ROUND(K88*$W$88*RANDBETWEEN(95,105)/100,0)","v":623},{"$f":"ROUND(L88*$X$88*RANDBETWEEN(98,102)/100,0)","v":699},"|","AY",3,1.5,1.1000000000000001,1,null,"AY",4.2,1.6,1.1000000000000001,1]
[null,null,{"$f":"C90-1","v":2017},{"$f":"ROUND(D88*RANDBETWEEN(80,120)/100,-2)","v":4300},{"$f":"ROUND(D89*$P$88*RANDBETWEEN(90,110)/100,-2)","v":14100},{"$f":"ROUND(E89*$Q$88*RANDBETWEEN(95,105)/100,-2)","v":21600},null,null,{"$f":"C89","v":2017},{"$f":"ROUND(D89*RANDBETWEEN(20,30)/1000,0)","v":103},{"$f":"ROUND(J89*$V$88*RANDBETWEEN(90,110)/100,0)","v":398},{"$f":"ROUND(K89*$W$88*RANDBETWEEN(95,105)/100,0)","v":624},null,"|"]
[null,null,{"$f":"C91-1","v":2018},{"$f":"ROUND(D88*RANDBETWEEN(80,120)/100,-2)","v":4500},{"$f":"ROUND(D90*$P$88*RANDBETWEEN(90,110)/100,-2)","v":13800},null,null,null,{"$f":"C90","v":2018},{"$f":"ROUND(D90*RANDBETWEEN(20,30)/1000,0)","v":99},{"$f":"ROUND(J90*$V$88*RANDBETWEEN(90,110)/100,0)","v":445},null,null,"|"]
[null,null,{"$f":"RANDBETWEEN(2019,2021)","v":2019},{"$f":"ROUND(D88*RANDBETWEEN(80,120)/100,-2)","v":5900},null,null,null,null,{"$f":"C91","v":2019},{"$f":"ROUND(D91*RANDBETWEEN(20,30)/1000,0)","v":124},null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","check",{"$f":"E88/D88","v":3},{"$f":"F88/E88","v":1.44},{"$f":"G88/F88","v":1.0787037037037037},null,null,"check",{"$f":"K88/J88","v":3.78},{"$f":"L88/K88","v":1.6481481481481481},{"$f":"M88/L88","v":1.1219903691813804}]
[null,null,"selected ultimate claims by AY",null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"E89/D89","v":3.2790697674418605},{"$f":"F89/E89","v":1.5319148936170213},null,null,null,null,{"$f":"K89/J89","v":3.8640776699029127},{"$f":"L89/K89","v":1.5678391959798994}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"E90/D90","v":3.0666666666666669},null,null,null,null,null,{"$f":"K90/J90","v":4.4949494949494948}]
[null,null,"AY","ult clms","  <===","sometimes you are not given the ultimate claims",null,null,null,null,null,null,null,"|","avg",{"$f":"AVERAGE(P92:P94)","v":3.1152454780361758},{"$f":"AVERAGE(Q92:Q94)","v":1.4859574468085106},{"$f":"AVERAGE(R92:R94)","v":1.0787037037037037},1,null,"avg",{"$f":"AVERAGE(V92:V94)","v":4.0463423882841356},{"$f":"AVERAGE(W92:W94)","v":1.6079936720640238},{"$f":"AVERAGE(X92:X94)","v":1.1219903691813804},1]
[null,null,{"$f":"C88","v":2016},{"$f":"ROUND(G88,0)","v":23300},null,"  - you would then have to calculate them using an appropriate method",null,null,null,null,null,null,null,"|","cum",{"$f":"P95*Q96","v":4.9934512800777027},{"$f":"Q95*R96","v":1.6029078014184397},{"$f":"R95*S96","v":1.0787037037037037},{"$f":"S95","v":1},null,"cum",{"$f":"V95*W96","v":7.3002224330663852},{"$f":"W95*X96","v":1.8041534137604376},{"$f":"X95*Y96","v":1.1219903691813804},{"$f":"Y95","v":1}]
[null,null,{"$f":"C89","v":2017},{"$f":"ROUND(F89*R$96,0)","v":23300},null,"  - see 2016.Spring #23",null,null,null,null,null,null,null,"|"]
[null,null,{"$f":"C90","v":2018},{"$f":"ROUND(E90*Q$96,0)","v":22120},null,null,null,null,null,null,null,null,null,"|",null,{"$f":"Q98*P88","v":4.95},{"$f":"R98*Q88","v":1.6500000000000001},{"$f":"S98*R88","v":1.1000000000000001},{"$f":"S88","v":1}]
[null,null,{"$f":"C91","v":2019},{"$f":"ROUND(D91*$P$96,0)","v":29461},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,"When selecting development factors, you may select a SIMPLE AVERAGE in this problem.",null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]

{"sheet":"4","index":4,"n_rows":60,"n_cols":28,"rows_kept":60,"cut":false,"hidden":false,"merged":[]}
["Reading:",null,"Friedland 17 (ULAE)",null,null,null,null,null,null,null,null,null,"Return to TOC","|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Model:",null,"2018.Spring #23",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem Type:",null,"Classical/Kittel approach for ULAE",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem",null,"Use the","classical",null,"approach to estimate the",null,null,"unpaid","ULAE","for AY",2020,null,"|","Step 1:",{"$f":"IF(D5=\"classical\",\"  classical ULAE ratio  ==>  (paid ULAE) / (paid claims)\",\"  Kittel ULAE ratio  ==>  (paid ULAE) / AVG [ (paid claims) , (incurred claims) ]\")","v":"  classical ULAE ratio  ==>  (paid ULAE) / (paid claims)"},null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,"occurrence",null,"  <==  policy type",null,null,null,null,null,null,null,"|",null,null,"paid",{"$f":"IF(D5=\"classical\",\"paid\",\"average\")","v":"paid"},"ULAE",null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"CY","ULAE",{"$f":"IF(D5=\"classical\",\"claims\",\"(pd, inc)\")","v":"claims"},"ratio",null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,"paid","paid","incurred","  <== incurred includes reported & IBNR",null,null,null,null,null,"|",null,{"$f":"P10-1","v":2016},{"$f":"E11","v":0},{"$f":"IF(D$5=\"classical\",F11,AVERAGE(F11,G11))","v":0},{"$f":"IFERROR(ROUND(Q9/R9,3),\"\")","v":""},null,null,null,null,null,null,null,null,"|"]
[null,null,null,"CY","ULAE","claims","claims",null,null,null,null,null,null,"|",null,{"$f":"P11-1","v":2017},{"$f":"E12","v":47000},{"$f":"IF(D$5=\"classical\",F12,AVERAGE(F12,G12))","v":403000},{"$f":"IFERROR(ROUND(Q10/R10,3),\"\")","v":0.11700000000000001},null,null,"Sometimes there is a trend in ULAE ratios.",null,null,null,null,null,"|"]
[null,null,null,2016,0,0,0,null,null,null,null,null,null,"|",null,{"$f":"P12-1","v":2018},{"$f":"E13","v":57000},{"$f":"IF(D$5=\"classical\",F13,AVERAGE(F13,G13))","v":327000},{"$f":"IFERROR(ROUND(Q11/R11,3),\"\")","v":0.17399999999999999},null,null,"If so, you may need to use judgement",null,null,null,null,null,"|"]
[null,null,null,2017,47000,403000,490000,null,null,null,null,null,null,"|",null,{"$f":"P13-1","v":2019},{"$f":"E14","v":59000},{"$f":"IF(D$5=\"classical\",F14,AVERAGE(F14,G14))","v":427000},{"$f":"IFERROR(ROUND(Q12/R12,3),\"\")","v":0.13800000000000001},null,null,"instead of just selecting the average",null,null,null,null,null,"|"]
[null,null,null,2018,57000,327000,480000,null,null,null,null,null,null,"|",null,{"$f":"D15","v":2020},{"$f":"E15","v":57000},{"$f":"IF(D$5=\"classical\",F15,AVERAGE(F15,G15))","v":451000},{"$f":"IFERROR(ROUND(Q13/R13,3),\"\")","v":0.126},null,null,null,null,null,null,null,null,"|"]
[null,null,null,2019,59000,427000,530000,null,null,null,null,null,null,"|",null,null,null,null,{"$f":"ROUND(AVERAGE(S10:S13),3)","v":0.13900000000000001},"  <== selected (average)",null,null,null,null,null,null,null,"|"]
[null,null,null,2020,57000,451000,400000,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 2:","  apply formula for unpaid ULAE",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,150000,"  case outstanding    (latest AY)",null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,80000,"  total IBNR    (latest AY)",null,null,null,null,null,null,null,null,"|",null,"unpaid ULAE",null,"=","(ULAE ratio)",null,"x",{"$f":"\"[ \"&D22*100&\"%   x\"","v":"[ 40%   x"},"( Case + IBNER )",null,"+","100%   x ","IBNYR ]","|"]
[null,null,null,0.75,"  % of total IBNR attributed to future case development on known claims",null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"where:",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,0.6,"  percent of unallocated work that occurs when a claim is opened",null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,0.4,"  percent of unallocated work that occurs when a claim is closed",null,null,null,null,null,null,null,null,"|",null,"IBNER","=",{"$f":"D19","v":0.75},"x","Total IBNR",null,"<== Incurred But Not ENOUGH Reported",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"=",{"$f":"R22","v":0.75},"x",{"$f":"D18","v":80000},null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"=",{"$f":"R23*T23","v":60000},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"IBNYR","=","Tot IBNR","-","IBNER",null,"<== Incurred But Not YET Reported",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"=",{"$f":"D18","v":80000},"-",{"$f":"R24","v":60000},null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"=",{"$f":"R27-T27","v":20000},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"therefore:",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"unpaid ULAE",null,"=",{"$f":"S14","v":0.13900000000000001},null,"x",{"$f":"\"[ \"&D22*100&\"%   x\"","v":"[ 40%   x"},{"$f":"D17+R24","v":210000},"+","100%   x ",{"$f":"R28","v":20000},"]","|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"unpaid ULAE",null,"=",{"$f":"S14*(D22*W32+Z32)","v":14456.000000000002},"  <== final answer",null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----"]

{"sheet":"5","index":5,"n_rows":60,"n_cols":28,"rows_kept":60,"cut":false,"hidden":false,"merged":[]}
["Reading:",null,"Friedland 17 (ULAE)",null,null,null,null,null,null,null,null,null,"Return to TOC","|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["Model:",null,"ULAE Example",null,null,null,null,null,null,null,null,null,null,"|","Step 1a"," calculate the claims basis B",null,null,null,null,null,null,null,null,null,null,null,"|"]
["Problem Type:",null,"Congor & Nolibos approach for ULAE",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,"claims","|"]
["Find",null,"Estimate the unpaid ULAE as of the latest given year-end using all 3 versions of the Congor and Nobilos approach.",null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,"basis","|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","CY",{"$f":"G10","v":0.5},"x","R","+",{"$f":"G11","v":0.35},"x","P","+",{"$f":"G12","v":0.15000000000000002},"x","C","B","|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",{"$f":"C19","v":2021},{"$f":"P6","v":0.5},"x",{"$f":"E19","v":55800},"+",{"$f":"T6","v":0.35},"x",{"$f":"F19","v":23900},"+",{"$f":"X6","v":0.15000000000000002},"x",{"$f":"G19","v":19800},{"$f":"P7*R7+T7*V7+X7*Z7","v":39235},"|"]
["Given",null,"independent estimate of ultimate claims for all AYs",null,null,null,null,423000,null,null,null,null,null,"|",{"$f":"O7+1","v":2022},{"$f":"P7","v":0.5},"x",{"$f":"E20","v":69200},"+",{"$f":"T7","v":0.35},"x",{"$f":"F20","v":29600},"+",{"$f":"X7","v":0.15000000000000002},"x",{"$f":"G20","v":24600},{"$f":"P8*R8+T8*V8+X8*Z8","v":48650},"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",{"$f":"O8+1","v":2023},0.5,"x",87900,"+",0.35,"x",36100,"+",0.15000000000000002,"x",31700,61340,"|"]
[null,null,"% of ULAE spend on opening claims",null,null,null,0.5,null,null,null,null,null,null,"|",2024,0.5,"x",111600,"+",0.35,"x",43300,"+",0.15000000000000002,"x",39900,76940,"|"]
[null,null,"% of ULAE spend on maintaining claims",null,null,null,0.35,null,null,null,null,null,null,"|",2025,0.5,"x",142800,"+",0.35,"x",52000,"+",0.15000000000000002,"x",49100,96965,"|"]
[null,null,"% of ULAE spend on closing claims",null,null,null,0.15000000000000002,null,null,null,null,null,null,"|",null,null,null,{"$f":"SUM(R7:R11)","v":467300},null,null,null,{"$f":"SUM(V7:V11)","v":184900},null,null,null,{"$f":"SUM(Z7:Z11)","v":165100},{"$f":"SUM(AA7:AA11)","v":323130},"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,"ultimate",null,"ultimate",null,null,null,null,null,null,"|","Step 1b"," select a ULAE ratio W:",null,null,"W  =  M / B",null,null,null,null,null,null,null,null,"|"]
[null,null,null,"paid","for clms","paid","for clms",null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,"ULAE","reported","loss","closed",null,null,null,null,null,null,"|",null,"paid","claims","ULAE",null,"If you decided at the beginning you are going to use a weighted average",null,null,null,null,null,null,null,"|"]
[null,null,null,"in CY","in CY","in CY","in CY",null,null,null,null,null,null,"|",null,"ULAE","basis","ratio",null,"for B then you only need the totals line in Step 1a and 1b. The problem with",null,null,null,null,null,null,null,"|"]
[null,null,"CY","M","R","P","C",null,null,null,null,null,null,"|","CY","M","B","W",null,"that however is that you may not see trends in the ULAE ratio.",null,null,null,null,null,null,null,"|"]
[null,null,2021,4500,55800,23900,19800,null,null,null,null,null,null,"|",{"$f":"C19","v":2021},{"$f":"D19","v":4500},{"$f":"AA7","v":39235},{"$f":"IFERROR(ROUND(P19/Q19,3),\"\")","v":0.115},null,null,null,null,null,null,null,null,null,"|"]
[null,null,2022,4500,69200,29600,24600,null,null,null,null,null,null,"|",{"$f":"O19+1","v":2022},{"$f":"D20","v":4500},{"$f":"AA8","v":48650},{"$f":"IFERROR(ROUND(P20/Q20,3),\"\")","v":9.1999999999999998E-2},null,null,null,null,null,null,null,null,null,"|"]
[null,null,2023,4700,87900,36100,31700,null,null,null,null,null,null,"|",{"$f":"O20+1","v":2023},4700,61340,7.6999999999999999E-2,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2024,4800,111600,43300,39900,null,null,null,null,null,null,"|",2024,4800,76940,6.2E-2,null,null,null,null,null,null,null,null,null,"|"]
[null,null,2025,5200,142800,52000,49100,null,null,null,null,null,null,"|",2025,5200,96965,5.3999999999999999E-2,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,{"$f":"SUM(P19:P23)","v":23700},{"$f":"SUM(Q19:Q23)","v":323130},{"$f":"IFERROR(ROUND(P24/Q24,5),\"\")","v":7.3349999999999999E-2},"  <=====","you can select this weighted average or choose another reasonable ratio",null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 2a"," calculate the estimate of unpaid ULAE using the Expected Claims approach",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"unpd ULAE","=","W","x","L","-","M",null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"=",{"$f":"R24","v":7.3349999999999999E-2},"x",{"$f":"H8","v":423000},"-",{"$f":"P24","v":23700},null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"=",{"$f":"R29*T29-V29","v":7327.0499999999993},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 2b"," calculate the estimate of unpaid ULAE using the Bornhuetter-Ferguson approach",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"unpd ULAE","=","W","x","(","L","-","B",")",null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"=",{"$f":"R24","v":7.3349999999999999E-2},"x","(",{"$f":"H8","v":423000},"-",{"$f":"Q24","v":323130},")",null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"=",{"$f":"R35*(U35-W35)","v":7325.4645},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Step 2b"," calculate the estimate of unpaid ULAE using the Development approach",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,"unpd ULAE","=","M","x","(","L","/","B","-",1,")",null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"=",{"$f":"P24","v":23700},"x","(",{"$f":"H8","v":423000},"/",{"$f":"Q24","v":323130},"-",1,")",null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,"=",{"$f":"R41*(U41/W41-1)","v":7324.9744684801781},null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|","Notes:"," You get the same answer for all 3 methods if your selection for W is the weighted average. You also have",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null," to keep enough decimal places or they may differ due to rounding.",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null," If you choose something other than the weighted average, which could be entirely reasonable depending",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null," on the circumstances then you won't in general get the same answer.",null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"|",null,null,null,null,null,null,null,null,null,null,null,null,null,"|"]
["----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----","----"]