The Optimal Reinsurance And Investment Problem Under Model Uncertainty

Recently, how to make the optimal strategies has became a hot issue in the research of the risk theory.Because the drift parameters in the random dynamic model of the insurance company’s asset prices is difficult to accurately estimate,to reduce the risk caused by the deviation of the estimated results from the real parameters,the insurance company’s agents wants to seek the robust optimal strategies. In this paper, it has strong reality significance we research the optimal reinsurance and investment problem under model ambiguity.The main contents of this paper are as follows:In Chapter 1, we introduce the research background of the optimal rein-surance and investment issues and overview of the model ambiguity.In Chapter 2, we mainly introduce the basic knowledge of the classical risk model, proportional reinsurance and excess-of-loss reinsurance and make necessary knowledge preparation for the following researchIn Chapter 3, based on the framework of Geometric Brownian Motion (GBM) market, we investigate the optimal reinsurance and investment prob-lem under model ambiguity. The surplus process of the insurer is assumed to follow diffusion risk model. If he is AAI (ambiguity-averse insurer)and has a specific preference for model ambiguity robustness.He hope to reduce the risk of possible model ambiguity by a robust strategy.With the aim of the insurer is to maximize the expected exponential utility of the terminal wealth,he consid-er robust optimal control problem under two different strategies as below:(i) The insurer can purchase reinsurance and invest in a financial market; (ii) The insurer can only invest in a financial market, but not purchase excess-of-loss reinsurance.Then, the explicit expressions for optimal strategies and optimal value functions for the conditions are derived by using stochastic control ap-proach.In Chapter 4, we investigate robust problem of the optimal excess-of-loss reinsurance and investment under Constant Elasticity of Variance(CEV) mod-el. The surplus process of the insurer is assumed to follow diffusion risk model . If he is ambiguity-averse and has a specific preference for model ambiguity robustness.The financial market consists of one risk-free asset and one risky asset whose price process satisfies CEV model. Adopting the stochastic con-trol approach,we derive explicit expressions of the optimal strategies and the corresponding value functionsIn Chapter 5, we investigate problem of the optimal excess-of-loss rein-surance and investment under model ambiguity and variance premium princi-ple. We consider an ambiguity-averse insurer whose surplus process of the in-surer is assumed to follow diffusion risk model.The financial market consists of one risk-free asset and one risky asset whose price process satisfies CEV model.Ambiguity-averse insurer buy a certain number of proportional reinsur-ance under variance premium principle. Adopting the stochastic control ap-proach,we derive explicit expressions of the optimal strategies and the corre-sponding value functions.