Guaranteed Optimization in Insurance of Catastrophic Risks

The proposed approach to the insurance of regionally distributed property against risk catastrophes is based on finding statistically robust coverage's of the insurance companies. Such coverage's guarantee that all companies survive no matter what scenario of the catastrophe from a given scenarios takes place. We describe a sequential algorithm that computed the minimum of the companies' premiums and finds optimal coverage's. A step of the algorithm is interpreted as searching a minimum-premium coverage that eliminates a current aggregate risk. The latter aggregates the risks of all companies with respect to all admissible catastrophe scenarios in a "fair" manner: the higher is the individual risk, the greater is its contribution to the aggregate risk. To justify the convergence of the algorithm we suggest a new global optimization procedure for a class of nonconvex minimization problems.