Are there any papers out there for optimizing what share an insurer should take on either a commercial policy or reinsurance treaty? Like the scenario would be, “The insurer only wants to take a %x share.” How is the share determined? Is that all just judgment based or is there something more algorithmic?
I don’t know about a paper. But I would think about this in terms of something like the following: The expected loss is X, but I want the probability of paying as much as Y to be probability p, and in no circumstances would I want to pay more than Z.
There’s related Exam 9 stuff on this.
But really it comes down to what you are trying to get out of reinsurance. Sometimes it’s locking in profit, sometimes it’s limiting per-property exposure, sometimes it’s eliminating catastrophic loss exposure. The cost of the reinsurance will come into play, too.
There are certainly metrics to be considered, like what a 1-100 year event looks like under different scenarios, or what the exposure does to your RBC.