I had to solve an interesting problem yesterday relating to pricing an excess layer which was contained in another layer which we knew the price for – I didn’t price the initial layer, and I did not have a gross loss model. All I had to go on was the overall price and a severity curve which I thought was reasonably accurate. The specific layers in this case were a 9m xs 1m, and I was interested in what we would charge for a 6m xs 4m.
Just to put some concrete numbers to this, let’s say the 9m xs 1m cost \$10m
The xs 1m severity curve was as follows:
I work as a pricing actuary at a reinsurer in London.