On the Design of Catastrophic Risk Portfolios

Ermoliev, Y.M., Ermolieva, T.Y., MacDonald, G.J., & Norkin, V.I. (1998). On the Design of Catastrophic Risk Portfolios. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-98-056

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Abstract

Catastrophes produce rare and highly correlated insurance claims, which depend on the amount of coverage at different 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 optimization model is discussed. Connections between ruin probability and nonsmooth, in particular concave, risk functions are established. Nonsmooth adaptive Monte Carlo optimization is proposed.

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