Optimal bonus strategies in life insurance: The Markov chain interest rate case

Abstract

We study the problem of optimal redistribution of surplus in life and pension insurance when the interest rate is modelled as a continuous time Markov chain with a finite state space. We work with traditional participating life insurance policies with payments consisting of a specified contractual payment stream and an unspecified additional bonus payment stream. Our model allows for interest rates below the technical interest rate. We apply stochastic control techniques in our search for optimal strategies, and we prove the dynamic programming principle for our particular type of problem. Furthermore, we state and prove a verification theorem and obtain an explicit solution that leads to a characterization of optimal strategies, indicating that some widely used redistribution schemes are suboptimal.