Research On Optimal Reinsurance-investment Policies For An Insurer With Mispricing Under Mean-variance Criterion

This thesis considers the optimal reinsurance-investment problems with mispricing stocks.With the help of the theory of stochastic control,dynamic programming principle and previous literatures,we derive the equilibrium strategies under different risk models.The mainly work of this paper are as follow:In Chapter 1,we introduce the research background,the significance of our problem and the latest research progress.Then,we present the mainly work and results of this thesis.In Chapter 2,we show several kinds of risk model,recommend the generation of mispricing in the risky market.In Chapter 3,we probe the optimal proportional reinsurance-investment strategy under classical risk model.Principle of expectation premium were adopted.The objective is to gain a strategy that maximize terminal wealth under mean-variance criterion.With the help of stochastic control theory we obtain the extend Hamilton-Jacobi-Bellman equations,derive the optimal strategies and the corresponding value function.Finally,we provide special cases and present numerical example to illustrate the effects of various parameters of the model on the optimal reinsurance and investment strategy.In Chapter 4,we probe the optimal excess-loss reinsurance-investment strategy under the diffusion approximation model.Principle of expectation premium were adopted.The objective is to gain a strategy that maximize terminal wealth under mean-variance criterion.With the help of stochastic control theory we obtain the extend Hamilton-Jacobi-Bellman equations,derive the optimal strategies and the corresponding value function.Finally,we present a numerical example to illustrate the effects of various parameters of the model on the optimal reinsurance and investment strategy.