A continuous time solution for optimal claim limits in vehicle insurance

Abstract

The traditional method of obtaining optimal claim limits for vehicle insurance is to discretise the state space and use successive approximations. In this paper we show how the stochastic dynamic programming equations reduce to a set of differential equations, in which these are easily solved to provide exact continuous time solutions. The resulting model can be used for evaluating alternative levels of excess.

Keywords:

• dynamic programming
• stochastic processes
• insurance