Insurer’s Portfolios of Risks: Approximating Infinite Horizon Stochastic Dynamic Optimization Problems

Many optimal portfolio problems, due to uncertainties with rare occurrences and the need to bypass so-called “end of the world effects” require considering an infinite time horizon. Among these in particular are insurer’s portfolios which may include catastrophic risks such as earthquakes, floods, etc. This paper sets up an approximation framework, and obtains bounds for a class of infinite horizon stochastic dynamic optimization problems with discounted cost criterion, in the framework of stochastic programming. The resulting framework is applied to an insurer’s portfolio of risk contracts.