Optimal Investment And Reinsurance To Reach A Bequest Goal Under Markov Regime Switching Model

This thesis examines optimal investment and reinsurance policies for an insurer to reach a bequest goal in a Markov regime switching market.It assumes that both the surplus process of the insurer and the financial market are drifted Brownian motions with coefficients modulated by an external Markov chain.The goal of the insurer is to maximize the probability that wealth before death meets a bequest goal l.The insurer pays dividend to shareholders with constant dividend rate c.We separately consider that the Markov chain is observable or not and adopt two methods to solve the optimization problem.When the Markov chain is observable,the method is to ap-ply Dynamic Programming Principles(DPP)and associated coupled Hamilton-Jacobi-Bellman(HJB)equations.In this case,we prove that,as long as the current state of the Markov chain is given,it is optimal for an insurer in a multiple-regime market to adopt the policies in the same way as in a single-regime market.Expelicit solutions to optimal polices are obtained when the insurer adopts proportional reinsurance and the premium is calculated in expectaion principle.We also provide numerical scheme for the approximating the value function of the control system and feedback optimal po-lices by Markov chain approximating method.When the Markov chain is unobservable,we assume the insurer is risk aversion and would like to seek robust control.In this case,the Markov regime switching is regard as a kind of "Knight uncertainty".That is,the goal of the insurer is to select optimal investment and reinsurance polices so as to maximize the probability of reaching a bequest goal in the "worst-case" scenario.By Girsanov transform for Markov chain,we formulate the optimal investment problems as a two player,zero-sum,stochastic differential game between the insurance company and the market.Verification theorems for the HJB solutions to the optimal investment problems are provided.