The Design of Optimal Insurance Decisions in the Presence of Catastrophic Risks

This paper deals with the development of decision making tools for managing catastrophic (low probability - high consequences) risks. Catastrophes produce rare and highly correlated claims, which depend on various decision variables, i.e., coverages at different locations, mitigation measures and reinsurance agreements. Joint probability distributions of these claims depicting their complex spatial and temporal interactions and effects of decision variables are analytically intractable. Spatial stochastic models of catastrophes can bypass these difficulties. Catastrophic models combine the simulation of realistic and geographically explicit catastrophic events with the differentiation of property values and insurance coverages in different locations of the region. Catastrophic models can be combined with stochastic optimization techniques to aid decision making on the spatial diversification of contracts, insurance premiums, reinsurance requirements, effects of mitigation measures, and the use of other financial mechanisms. The aim of this paper is to extend a two-stage spatial catastrophic model to dynamic cases reflecting dependencies of risk accumulation processes in time. This extension is important since it can be used for the analysis of decisions under changing frequencies of events and values of properties. It is also possible to incorporate catastrophes caused by the clustering in time of such events as rains and droughts due to persistence in climate. The model can be used by individual insurers, pools of insurers or regulatory authorities.