Run Off Triangles - Sept 05 Question 9

[WelshBird]

Can anyone explain?

Question 9 (ii) of the September 2005 paper asks for the application of the Bornhuetter-Ferguson method to estimate the outstanding claims arising from policies written in 2004 whilst taking inflation into account.

For accident year 2004, I applied the development factors to the expected ultimate loss to find the expected claims paid to date (of 1,558,3). I thought the next step would be to compare this to the actual claims paid to date (of 1,480) and adjust the expected claims in subsequent years accordingly. However, no adjustment is made in the answer to the question.

Am I missing something?

 

[Anna Bishop]

Hello WB

Your method is not wrong, but it needs modifying for inflation!

The expected amount of 1558.3 is high relative to the actual amount of 1,480.

In fact it is 78.3 too high, so we should reduce our initial ultimate estimate of 3937.5 (5250 * 0.75) by 78.3 to 3859.2.

But this is the revised ultimate estimate of claims incurred in 2004 monetary terms! However, some of this figure of 3859.2 will be incurred in 2004, some in 2005, some in 2006 and some in 2007. We need to be able to break down the 3859.2 into the separate years in which it is expected to be incurred so that we can apply the relevant future inflation.

Of the 3859.2:

1,480 is actually incurred in 2004
1149.8 is expected to be incurred in 2005
770.0 is expected to be incurred in 2006
459.4 is expected to be incurred in 2007

To get these numbers, I have done:

1149.8 = [3937.5 / (1.284342 * 1.132074) - 78.3] - 1480
770.0 = [3937.5 / 1.132074 - 78.3] - 1480 - 1149.8
459.4 = [3937.5 - 78.3] - 1480 - 1149.8 - 770.0

We can then look at what these claim amounts will be in the relevant future years.

1149.8 is expected to be 1149.8 * 1.025 = 1178.5 in 2005
770.0 is expected to be 770.0 * 1.025^2 = 809.0 in 2006
459.4 is expected to be 459.4 * 1.025^3 = 494.7 in 2007

These sum to 2482, which is the answer given in the examiners' report.