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...

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...

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...

A convex nonsmooth optimization problem is replaced by a sequence of line search problems along recursively updated rays. Convergence of the method is proved and applications to linear inequalities, constraint aggregation and saddle point seeking indicated.

A general constraint aggregation technique is proposed for convex optimization problems. At each iteration a set of convex inequalities and linear equations is replaced by a single inequality formed as a linear combination of the original constraints. After solving the simplified subproblem, new...