Optimal debt ratio and dividend strategies for an insurer under a regime-switching model

This paper studies the optimal debt ratio and dividend strategy for an insurer under the model with the coefficients depending on the state of the economy. The object is to maximize the total expected discounted utility of dividend payment of the insurer. The optimal strategy and value function are characterized by the classical solution of the associated Hamilton-Jacobi-Bellman equation which can be reduced to a system of nonlinear PDEs. Considering logarithmic and power utility, we show the existence of classical solution to the system by the ordered upper-lower solution method, and verify that the solution is indeed the value function.