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...

The paper proposes for the general framework for the optimization capacity of an insurance industry in responding to catastrophic risks. Explicit geographical representation allows for sufficient differentiation of property values and insurance coverages in different parts of the region and for...

New types of laws of large numbers are derived by using connections between estimation and stochastic optimization problems. They enable one to "track" time-and-path dependent functionals by using, in general, nonlinear estimators. Proofs are based on the new stochastic version of the Lyapunov's...

Recently we analyzed important classes of nonsmooth and nonconvex risk control problems which can not be solved by standard optimization techniques. The aim of this article is to develop computational procedures enabling us to bypass some of the obstacles identified in this paper. We illustrate...

A stochastic version of the branch and bound method is proposed for solving stochastic global optimization problems. The method, instead of deterministic bounds, uses stochastic upper and lower estimates of the optimal value of subproblems, to guide the partitioning process. Almost sure...

This note deals with on-line computation or learning of Pareto optimal insurance contracts. We account for the fact that the loss distribution often is unknown, unavailable, or intractable. Alternatively, the contracting parties could be inexperienced. In both cases loses must be simulated or...

The paper describes how stochastic optimization techniques can be used to model profit maximizing producer behavior in a spatial continuum. The main methodological issues to be addressed are, first, that the representation of optimal allocations in a spatial continuum naturally lead to models...

The proposed approach to the insurance of regionally distributed property against risk catastrophes is based on finding statistically robust coverages of the insurance companies. Such coverages guarantee that all companies survive no matter what scenario of the catastrophe from a given scenarios...

Owners of stochastic assets can pool their endowments to smoothen and insure individual payoffs across outcomes and time. We explore, in such a setting, how contingent shadow prices on aggregate resources can be used for three purposes: First, to design mutual contracts for risk averse agents;...