Risk-minimizing portfolio selection for insurance payment processes under a markov-modulated model

This paper extends the model in Riesner (2007) to a Markov modulated Ĺevy process. The parameters of the Ĺevy process switch over time according to the dierent states of an economy, which is described by a finitestate continuous time Markov chain. Employing the local risk minimization method, we find an optimal hedging strategy for a general payment process. Finally, we give an example for single unit-linked insurance contracts with guarantee to display the specific locally risk-minimizing hedging strategy.