Optimization methods for compound Poisson risk processes

In this article we introduce the notion of the family of compound Poisson risk processes that depend on a finite-dimensional parameter; we describe examples of such families that arise during formalization of surplus, quota, and quota-surplus reinsurance contracts; the optimization problem is stated for the growth rate of insurance company capital subject to a given constraint on the probability of ruin; numerical methods for solving this problem by Lagrange function saddle-point techniques are reviewed.