Hi, When solving chapter 26.10, I was very confused with the time periods that are being used. The question asks us to build the revenue account with discounted reserves. There is no mention of the timing of claim settlements/payments etc and thus, I would guess that the assumptions would play a very important role here. The main assumption made is that premiums are written uniformly (and earned evenly) - this is reflected correctly in the earned premium calculations. However, when discounting reserves (that are b/f and c/f), the bookwork discounts the claim payments of the next year by 0.5 and the claim payments for the year after by 1.5. Discounted claims reserves at 1/1/X+2: (561+1005)/(1.08^05) + 1005/(1.0-8^1.5) Discounted claims reserves at 31/12/X+2: (1005+1116)/(1.08^0,5)+ 1116/(1.08^1.5) Thus, for reserves as at 1/1/X+2 (reserve b/f for year X+1), the claims reserve for year X+2 are discounted by 0.5 and claim reserve for payments in X+3 are discounted by 1.5. However, how is 0.5 correct here? If we assume that the policies were written evenly, the average start of the policy would be 1/7/X for year X and 1/7/X+1 for year X+1 and so on. Average claim occurrence would therefore be 1/1/X+1 for claims in year X and so on. Assuming no settlement delay, shouldn't we use 1 (instead of 0.5) for discounting the next year reserves and 2 (instead of 1.5) for discounting reserves of the subsequent year?
I think you are asking about Question 27.10 as there is no Question 26.10 We have assumed earlier that "claims occur on average in the middle of each year". Then for example, we know that in calendar year X+2 564 will be paid from origin year X, this then needs to be discounted by 0.5 years when determining the reserve at the start of year X+2 and so on.
@Darren Michaels my apologies. However, if we assume that the policies are written on average in the middle of the year, then does the assumption that claims on average occur in the middle of the year make sense? Would that be an acceptable assumption to make? Also, is the assumption claims on average occur at the end of the year (because policies are written in the middle of the year) an accurate assumption to make here?
I think you are confusing what we are trying to do here. In this part of the question we have worked out what claims we expect to arise in calendar year X+2 from each origin year. These claims will have arisen from policies not just written in X+2, but also those written in X+1 and, X. We are then saying that those claims that do arise in year X+2, will arise uniformly over that year, and so on average will arise in the middle of that year, hence the 0.5 years' worth of discounting. Your approach is looking at all of the claims arising from the business written in X+2, irrespective of when they emerge.
