Marsh Insurance Risk Model Under The Dynamic Modulation Strategy Selection Problem

The premium rate of the unit time, the arrival intensity of claims and claim size distribution of the insurance company depend on the state of the environment or the economy. Therefore, it is very important in the theory and practicas to study the strategy selection problem under the the classical compound Poisson risk model with regime switching.In this paper we study the optimal reinsurance and investment strategies selection problem of the company under the classical compound passion risk model with regime switching. First, we consider the continuous-time dynamic mean-variance proportional reinsurance selection problem. By adopting the Hamilton-Jocobi-Bellman (HJB) equation and the Langrange multiplier technique, we obtain the expressions of the optimal proportional reinsurance strategy and the mean-variance efficient frontier in closed forms. Secondly, we study the continuous-time dynamic mean-variance proportional selection problem under the classical compound passion risk model with regime switching. By using the techniques of the stochastic linear-quadratic control, we obtain the closed-forms expression of the optimal portfolio strategy and the efficient frontier. Finaly, we study the portfolio selection problem of maximizing expected utility of the terminal surplus. We also obtain the explicit expression of the optimal portfolio strategy and the maximum expected utility of the terminal surplus.