Optimal Investment And Reinsurance Under Markov Regime Switching Model With High Gain Tax

In this thesis,optimal investment and reinsurance policies for an insurer who subject to the payment of high gain tax are investigated,where the object of the insurer is to maximize the expected terminal utility.The surplus process and the return process of financial market are both assumed to be jump diffusion process and were modulated by an external Markov chain,which specifies the variable of the macroeconomic environment.We prove that the value function of our control problem is the viscosity solution to the associated coupled HJB equations.By finite difference method and weak convergence theory of Markov chain,we present numerical method for approximating the value function.Together with the feedback control expressions,we also present the numerical method of obtaining optimal control policies.Two numerical examples are given to illustrate the impacts of high gain tax and regime switching on optimal policies.