Hi everyone, I have purchased the ASET for this paper but still don't quite understand the different approaches. My current understanding is as follows: Approach 1: You fix the CoV, apply this to the new lower best estimates, so the distribution will be less spread out and less extreme. Approach 2: You increase the CoV, apply this to new lower best estimates, so new distribution generally increases faster as compared to the previous distribution. So the difference between the high and best estimates are the same in absolute amounts in the previous and new distributions. However, I'm not sure why it mentions that historical margins will be the same percentile as they were previously? Approach 3: You increase CoV, apply this to the new lower best estimates and fix the amount at the specified return period. So the difference between the high and best estimates are the different in absolute amounts in the previous and new distributions i.e the difference is higher in the new distribution. However, I'm not sure why it mentions that historical margins will appear to be at a lower percentile than they were previously. Is my above understanding correct/ in the right direction? Any advice is appreciated and thanks in advance
Hi Laura, Approach 1: Yes that's right, well done. You're asked to reparameterise the lognormal distribution using the best estimate reserve as the mean. We have CoV(old) = sd/mean(new)... Solving for sd gives a lower standard deviation, simply because the mean will be lower. Approach 2: The absolute value of the reserve risk (ie high - best estimate) is unchanged. Now let's think what effect this would have: We know the mean, that's just the best estimate reserve. We also know the high estimate ... let's assume that we calculated this as the 99.5th percentile. That gives us two equations (the mean and the 99.5th %ile) to solve two unknowns - the parameters of the lognormal distribution. The CoV by definition is a measure of the spread of the distribution relative to the mean. Here we have the same 'spread' as before, but now divided by a lower mean. So yes, you're right, this approach must mean that the CoV increases. We can see that the 99.5th percentile must remain the same because we were forced to assume so when we reparameterised the lognormal distribution. Approach 3: It's hard to know what the examiners were aiming at for Approach 3, their description isn't very clear in my opinion. This is not the first time that we GI tutors here at ActEd have looked at it and we are still none the wiser. Perhaps there are some clever clogs out there who can answer your question.
