F2016#16a
for the expiring pol, since entry ratio = 1 is derived from using agg ded of $300K, why didn't we use the corresponding charge% of 0.365 from table M? Similarly, for Option 1. Thank you!
for the expiring pol, since entry ratio = 1 is derived from using agg ded of $300K, why didn't we use the corresponding charge% of 0.365 from table M? Similarly, for Option 1. Thank you!
Comments
We're using a Limited Table M approach here. For the expiring policy, the loss in excess of the per-occurrence deductible (XL) is E[A] - E[A_D] = 40%*500000 = 200000. We then add on the expected loss in excess of the aggregate deductible using the modified (limited) table M.
The limited table M entry ratio is the aggregate deductible / E[A_D] = 300,000 / 300,000 = 1. The limited table M is indexed by entry ratio and the per-occurrence deductible which is why we use the 100,000 column instead of the 300,000 column for the expiring policy.
Similarly, for Option 1 we use the 200,000 column for the per-occurrence deductible and the limited table M entry ratio is now the aggregate deductible of 400,000 / E[A_D] = 1 as E[A_D] = (1-20%)*500,000 = 400,000.
in part b solution's 1st bulletin point"
"Option 2 does not list an aggregate retention limit and so will be more protected against losses increasing above this (in aggregate)"
I thought by not having an aggr retention limit, insurer will bear more losses as the insureds only bear losses under the retention limit. So the insurers are in a more adverse position for this option. Where did I get it wrong?
In Option 2, the insured is responsible for the first $200,000 of losses for each occurrence. If this option also had an aggregate retention of say $400,000 then the insured is only responsible for up to $400,000.
So, for example, if there were losses of $100,000; $300,000 and $700,000 then without the aggregate retention the insured covers $100,000; $200,000 and $200,000 while the insurer covers $100,000; $100,000 and $500,000.
With the above aggregate retention the insured covers $100,000, $200,000 and $100,000 (for a total of $400,000) and the insurer covers $100,000; $100,000 and $600,000.
So the insurer is in an more adverse position when there is an aggregate retention. I think you mixed up who the aggregate retention applies to. It applies to the amount retained by the insured, not the insurer.
The upward trend in the ground up losses in this question means if there was an aggregate retention it would be exhausted quicker. So not having an aggregate retention is a good thing for the insurer.