Research On Optimal Investment And Reinsurance Strategies With Random Time Exit

This thesis mainly uses stochastic control theory,dynamic programming principle,stochastic analysis and other mathematical tools to study investment and reinsurance problems of ambiguity-aversion insurers with random time exit under the diffusion approximation of the classic risk model and the dual dependent claim risk model.The main research contents of this thesis are as follows:In chapter 1,we introduce the research background,the significance of our problem and research status of the research,and briefly describe the main contents of this paper.In chapter 2,we mainly show the financial market and various risk models.In chapter 3,we study the robust optimal investment-reinsurance strategy of insurers under the diffusion approximation of the classic risk model with random time exit.Market supervision prohibits insurers from short-selling but allows lending to banks,and the loan ratio cannot exceed a fixed level.Insurers transfer risk by purchasing proportional reinsurance.We aim to minimize the probability that the insurer’s wealth process reaches a high level before hitting the lower bound for the first time.Using the principle of dynamic programming,we derive an optimal investment-reinsurance strategy and closed-form expression of the corresponding value function by solving the Hamilton-JacobiBellman(HJB)equation.Finally,we discuss the influence of parameters on the optimal investment-reinsurance strategy through numerical analysis.In chapter 4,we study the robust optimal investment-reinsurance strategy of insurers under the diffusion approximation of the dual dependent claim risk model with random time exit.The optimization objective is to minimize the probability that the insurer’s wealth process reaches a high level before hitting the lower bound for the first time.Using the principle of dynamic programming,we obtain the optimal control strategy and the explicit solution of the value function by solving the HJB equation.Finally,we discuss the influence of parameters on the optimal investment-reinsurance strategy through numerical analysis.