Aggregate Reinsurance Question

[Sleepy]

This is the situation:

12 month policy. Pricing reinsurance for 500K cover above an aggregate of 750K.

If the policy was then being switched to 6 months, how would this effect the pricing. Still going to offer a 500K cover but it will be excess of an aggregate of 375K. Still the same exposure of the 500K but it would be a higher rate since it is only above 375K BUT it is now only a 6 month policy so not as long of a period to reach the aggregate. How does the change to 6 months come into play for the pricing?

[Colymbosathon ecplecticos]

Simple answer: The six month policies extend much more cover.

To see this, suppose at one extreme that losses are very infrequent, but when they do happen they are 750 ground up.

The first cover pays none of this, the second pays 375.

At the other extreme consider a constant loss process at a rate of 1750/year.

The first cover will pay 500. The second cover will pay 500 twice (once in each policy period).

[Sleepy]

Would one assume that is the expected loss is 600K for the full year, it would then only be 300K for the 6 month period...assuming losses evenely through the year?

It breaks down to 500K x 375 in 6 months and 500K x 750K in 12 months. The probablility it higher for >375K, even with only a 6 month period to reach it then the >750K in 12 months. Is that right?

[Colymbosathon ecplecticos]

I would suggest that you make a simple simulator in a spreadsheet. Use a frequency-severity model and see what happens for yourself.