Friedland14.Recoveries

Chapter 14: Recoveries: Salvage and Subrogation and Reinsurance

Reading: Friedland, J.F., Estimating Unpaid Claims Using Basic Techniques, Casualty Actuarial Society, Third Version, July 2010. The Appendices are excluded.

BattleTable

Based on past exams, the main things you need to know (in rough order of importance) are:

• (Reinsurance)

   - understand mechanics of quota-share (Q/S), excess-of-loss & stop-loss reinsurance

   - calculating ultimate claims net of reinsurance using net/gross/ceded loss triangles and appropriate tail factors

• (Salvage/Subrogation)

   - calculating ultimate salvage & subrogation using either the development method or the ratio method

   - selecting the best method, knowing the advantages & disadvantages of each

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Spring #21)	(Reins) identify scenario: - high reported claims	(Reins) ultimate: - discuss approaches
E (2019.Spring #23)	(Reins) retained IBNR: - rptd devlpt method
E (2018.Spring #22)
E (2017.Fall #16)	(Reins) CYEP: - calculate	(Reins) gross UEP: - calculate	(Reins) reported claims: - calculate AY value
E (2017.Fall #25)	(Reins) net unpaid claims: - reptd devlpt method
E (2016.Fall #24)	(S/S) ultimate S/S: - devlpt method	(S/S) ultimate S/S: - ratio method	(S/S) ultimate S/S: - any method
E (2015.Fall #23)	(Reins) net PY IBNR: - calculate	(Reins) net PY unpd clms: - calculate
E (2015.Spring #24)	(S/S) net ultimate clms: - ratio method
E (2014.Fall #21)	(Reins) reins program: - determine structure	(Reins) ceded IBNR: - calculate
E (2014.Spring #20)	(S/S) ultimate S/S: - ratio method
E (2013.Fall #22)	(Reins) net data: - assess reasonableness	(Reins) ultimate clms: - net/gross/ceded	(Reins) tail factors: - impact of Q/S & stop-loss
E (2013.Spring #24)	(S/S) ultimate S/S: - devlpt method	(S/S) ultimate S/S: - ratio method	(S/S) ultimate S/S: - best method

In Plain English!

Intro

• when using the terms net, gross, ceded, you have to be clear what they apply to...
• net means either net of S/S, net of reinsurance, net of cats (make sure you know which before flying off on your calculations)

Salvage/Subgrogation Recoveries

Alice-the-Actuary has decreed that we will henceforth use S/S as an abbreviation for Salvage/Subgrogation. (And I will henceforth ask our good friend Alice to stop using pretentious vocabulary such as "decreed" and "henceforth".)

Here is an old exam problem asking you for the ultimate S/S using both the development method and the ratio method:

E (2016.Fall #24)

The development method for S/S is exactly the same as the development method for any other triangle of loss data. I have included the result of the development method in my solution below but have omitted the intermediate steps. (Alice says you should know how to do that by now.) The solution shows the details for the ratio method:

S/S Ratio Method - 2016.Fall #24(b)

Reinsurance Recoveries

The source text (Friedland) has 3 very nice, simple examples of the different types of reinsurance you need to understand. (Links provided below.) The 3 types of reinsurance discussed in the text are:

1. quota-share
2. excess-of-loss
3. stop-loss

You're probably at least somewhat familiar with these different forms of reinsurance, but let's cover the key points in simple terms.

Quota-share reinsurance is a pro-rata contract where the insurer and reinsurer share premiums and losses according to a fixed percentage.

Suppose you have a gross loss of $1,000. If you also have a quota-share reinsurance treaty with a quota-share percentage of 70% then:

• net loss (net of quota-share reinsurance) = $1,000 x 70% = $700
• ceded loss = $1,000 x 30% = $300

The allocation of gross premium works the same way. If the gross premium received by the reinsurer is $200, then the net premium is $200 x 70% = $140, and the ceded premium is $70.

On its own, this is very easy to understand. But remember: the quota-share percentage is applied to the gross loss to get the net loss. Confusion sometimes arises when the quota-share percentage is very low, like 25%. People sometimes think that means 25% of the gross loss is the ceded loss. That's wrong! (Multiply the gross loss by 25% to get the net loss.)

Here's a quick link to the Friedland's example of quota-share reinsurance:

Example: Quota-Share (source text)

Note that if you have the gross and net loss triangles, it's very easy to determine whether or not you've got a quota-share contract.

Excess-of-Loss reinsurance indemnifies the ceding company for losses that exceed a specified limit. (It is non pro-rata reinsurance.)

The contract would state whether the specified limit applies separately to individual losses or to aggregate losses.

Suppose a primary insurer has 2 claims for the amounts of $100 and $175.

Example 1: apply the individual limit of $150 to each individual loss

• loss 1 = $100→ no reinsurance recovery because loss ≤ $150
• loss 2 = $175→ reinsurance recovery = (loss 2) - limit = $175 - $150 = $25
• total recovery = $0 + $25 = $25

Example 2: apply the aggregate limit of $150 to aggregate losses

• aggregate loss = (loss 1) + (loss 2) = $100 + $175 = $275
• total recovery = (aggregate loss ) - limit = $275 - $150 = $125

Below is a link to the Friedland's individual excess-of-loss reinsurance example. The attachment point is $1m. That means all claims under $1m are covered by the primary insurer and the excess over $1m is covered by the reinsurer. The example doesn't provide details of individual claims but at least you can see how the triangles are different the quota-share example. AY 2005 & 2007 had individual claims over $1m (as you can deduce from the ceded loss triangle) while AY 2006 & 2008 did not have any claims over $1m.

Example: Excess-of-Loss (source text)

Note: Friedland generally uses the term excess-of-loss reinsurance for individual excess-of-loss reinsurance, and stop-loss reinsurance for aggregate excess-of-loss. (See below.)

Stop-Loss reinsurance indemnifies all losses above a specified amount during the contract period.

This is really just the same as aggregate excess-of-loss, but we'll look at a more slightly more complicated example:

• you can apply the stop-loss limit/attachment point on top of the net losses from an individual excess-of-loss policy

→ text example has individual claim attachment point = $500,000

• the contract can apply to AYs, PYs, CYs (Accident Years, Policy Years, Calendar Years)

→ text example applies to PYs

• the stop-loss limit/attachment point can be applied across multiple years and coverages

→ example combines 3 PYs: 2002/03, 2003/04, 2004/05

• there is often an upper limit on recoveries (beyond which the primary insurer again becomes fully responsible)

→ text example does not have an upper limit

Make sure you can follow the example below.

Example: Stop-Loss (source text)

Alice created a few more practice examples of stop-loss reinsurance similar to the example from Friedland.

2 Stop-Loss practice problems