Optimal investment and reinsurance strategies for an insurer with regime-switching

This paper considers the issue of optimal investment and reinsurance strategies for an insurer with regime-switching. In our mathematical model, a risk-free asset and a risky asset are assumed to rely on a continuous time-homogeneous, finite-state, observed Markov chain, and the latter’s price dynamics is described by a general regime-switching jump-diffusion process. We are extending the classical claim process to a Markov-modulated compound Poisson process. The insurer faces the decision-making problem of choosing to invest his/her surplus in the financial market and purchase reinsurance such that the expected power utility of his/her terminal wealth is maximized. We apply dynamic programming principle to derive the regime-switching Hamilton–Jacobi–Bellman (HJB) equation. Then, by analysing the solutions of the HJB equation, the optimal investment and reinsurance strategies are obtained and given in the verification theorem. Finally, the numerical analysis based on a two-state Markov chain is presented to illustrate our results.