View source for Bornhuetter-Ferguson Formula Proof

Prove that the following 2 formulations of the reported Bornhuetter-Ferguson method are equivalent:

'''Formulation 1''':
* Ult<sub>r-BF</sub> &nbsp; = &nbsp; z x Ult<sub>r-Dev</sub> + (1 &ndash; z) x Ult<sub>ECR</sub>
: ''where z &nbsp; = &nbsp; %reported &nbsp; = &nbsp; 1/CDF''

'''Formulation 2''':
* Ult<sub>r-BF</sub> &nbsp; = &nbsp; (reported claims) + (1 &ndash; 1/CDF) x Ult<sub>ECR</sub>

'''Proof''':

Starting with Formulation 1 and using the fact that Ult<sub>r-Dev</sub> = (reported claims) x CDF, we have:

* Ult<sub>r-BF</sub>
: = &nbsp; z x Ult<sub>r-Dev</sub> + (1 &ndash; z) x Ult<sub>ECR</sub>
: = &nbsp; 1/CDF x (reported claims) x CDF + (1 &ndash; 1/CDF) x Ult<sub>ECR</sub>
: = &nbsp; (reported claims) + (1 &ndash; 1/CDF) x Ult<sub>ECR</sub>

And the last line is Formulation 2. Since these steps are reversible, we can conclude that Formulation 1 and Formulation 2 are equivalent.