Fair pricing of participating life insurance contracts in a regime-switching market environment

In this thesis we present a framework in which participating life insurance contracts can be valuated and analyzed in a regime-switching market environment. In particular, we let the asset process (modeling the insurer's asset portfolio) evolve according to a geometric Brownian motion whose coefficients depend on a continuous-time Markov chain with finite state space. The influence of the Markov chain results in the market model being incomplete and in the fact that the equivalent martingale measure frequently used for pricing purposes is not unique. We provide a characterization of equivalent martingale measures based on the Esscher measure (see for example Elliott et al. [9]). The insurance pricing problem can be equivalently formulated as an infinite-dimensional linear program (LP), the solution of which has to be determined numerically. We introduce an approach based on a discretization of the state space and a Markov chain approximation as well as a moment approach which uses conditions introduced by Hausdorff [10] to formulate the linear program in terms of moments of measures.