PROBLEM
Suppose that a client (a primary insurance company) is asking a reinsurance
company for protection for cases when losss ratio exceeds a certain number,
the reinsurer would pay losses uo to certain amount. The client has
provided you, say, loss ratios for the last 5 years. The question is: as a
reinsurer, how would you price for this coverage?
MY INITIAL THOUGHT
My initial thought was to fit an appropriate probability using the loss
ratio data provided by the client and then simulate random numbers from the
fitted model. And pricing would be based on this simulated data set.
PROBLEMS WITH MY APPROACH
(i) Normally, the data set provided by the client is more or less flat;
that is, there is not much random variation in the data set. The only
distribution you can fit is a Uniform distribution.
(ii) The reinsurer would be hit only when the loss ratio is very high; this
would only occur when there is a catastrophe (which may happen, say, once
in 50 years).
(iii) Even if there are variations in the data set provided by the client
and you fit an approximate model to the data set - you simulate data from
the fitted model, the problem is that the loss ratio coverage wanted by the
client is very high (that is, his past past experience says, average loss
ratio is, say 90% - but the primary company wanted coverage, say, when loss
ratio exceeds 120%) - pricing model based on expected loss cost would be
ridiculous. It would underprice the reinsurance coverage. We are in a
situation where the probability of actual loss ratio would exceed the
coverage loss ratio is very small (as the probability of a catastrophe is
very small - but if the event occurs, the loss would be very high).
I would be interested in getting any ffedback, any kind of reference or any
other source that may be useful to me and also to others who may be
interested in this area. I am also interested to know how others are
pricing in these situations.
Thank you.