Optimal pooling strategies under heterogeneous risk classes

Abstract

The purpose of this paper is to determine optimal pooling strategies from the perspective of an insurer's shareholders underlying a default probability driven premium loading and convex price-demand functions.,The authors use an option pricing framework for normally distributed claims to analyze the net present value for different pooling strategies and contrast multiple risk pools structured as a single legal entity with the case of multiple legal entities. To achieve the net present value maximizing default probability, the insurer adjusts the underlying equity capital.,The authors show with the theoretical considerations and numerical examples that multiple risk pools with multiple legal entities are optimal if the equity capital must be decreased. An equity capital increase implies that multiple risk pools in a single legal entity are generally optimal. Moreover, a single risk pool for multiple risk classes improves in relation to multiple risk pools with multiple legal entities whenever the standard deviation of the underlying claims increases.,The authors extend previous research on risk pooling by introducing a default probability driven premium loading and a relation between the premium level and demand through a convex price-demand function.