Hi Tutors, I am not quite understanding the solution below; "The expected claims under the new ‘7xs3’ policy is $23.0m (undiscounted) so the expected claims size for one additional claim under the new policy is $0.86m which is reasonable compared to an average expectation of $1m. The average expectation is $1m because the additional loss now covered by the new policy must be between $3m and $5m so the payout for ABC Re would average $1m." How is the $0.86m being calculated as well as the $1m average expectation? Kind regards,
The first thing to say here is that any check on the results would have been acceptable here, and it didn't have to be the calculation outlined below. Don't get too caught up in the details of this particular one. However, here is the explanation of this particular calculation. The examiners are carrying out a reasonableness check on the results for the new scenario by trying to estimate the new claim costs based on the original work. The retention level has reduced under the new 7xs3 cover, so the reinsurer is now paying claims between 3-5m that they weren't before. So, we now expect an extra 2m of exposure and based on the claim frequency from the original work, we would estimate the cost of this as 2m x 3.9 = 7.8m of EXTRA claims. We can use this to estimate the TOTAL expected claims under the new 7xs3 cover, which would be 14.3m + 7.8m = 22.1m. However, this is just based on claims that would have been made under the old level of cover. Under the new level of cover the actual expected claims are 23m. The difference between these is around $0.86m if you use exact values (as in Excel). This must come from additional claims that are now being covered that the reinsurer was not previously told about (so are not included in the 22.1m estimate we have made). This arises because the retention limit has now reduced from 5m to 3m. So, we are covering an additional 2m of claims, and on average we would expect this to lead to an additional 1m of claims that we didn't previously know about. So, the $0.86m is reasonably close to this. As I said at the start of the reply - this is just one approach, and any reasonable method of confirming that the results would be fine.
