Stochastic optimization of insurance portfolios for managing exposure to catastrophic risks

A catastrophe may affect different locations and produce losses that are ra re and highly correlated in space and time. It may ruin many insurers if th eir risk exposures are not properly diversified among locations. The multid imentional distribution of claims from different locations depends on decis ion variables such as the insurer's coverage at different locations, on spa tial and temporal characteristics of possible catastrophes and the vulnerab ility of insured values. As this distribution is analytically intractable, the most promising approach for managing the exposure of insurance portfoli os to catastrophic risks requires geo graphically explicit simulations of c atastrophes. The straightforward use of so-called catastrophe modeling runs quickly into an extremely large number of "what-if" evaluations. The aim o f this paper is to develop an approach that integrates catastrophe modeling with stochastic optimization techniques to support decision making on cove rages of losses, profits, stability, and survival of insurers. We establish connections between ruin probability and the maximization of concave risk functions and we outline numerical experiments.