On the Design of Catastrophic Risk Portfolios

Catastrophes produce rare and highly correlated insurance claims, which depend on the amount of coverage at di#erent locations. A joint probability distribution of these claims is analytically intractable. The most promising approach for estimating total claims for a particular combination of decision variables involves geographically explicit simulations of catastrophes. The straightforward use of catastrophe models runs quickly into infinite "if -- then" evaluations. The aim of this paper is to develop a framework allowing for the use of Monte Carlo simulation of catastrophes to aid decision making on designing optimal catastrophic risk portfolios. A dynamic stochastic optimization model is discussed. Connections between ruin probability and nonsmooth, in particular concave, risk functions are established. Nonsmooth adaptive Monte Carlo optimization is proposed. Keywords: Catastrophes, Insurance, Risk, Stochastic optimization, Adaptive Monte Carlo, Nonsmooth optimization, Ruin proba..