Dynamic Investment And Several Classes Reinsurance Problem Under Expect Utility

In recent years, the optimal investment and reinsurance problems have be-come the significant issues in the finance, the insurance company need to invest in financial markets to survive, and purchase a certain amount of reinsurance to reduce the risk. The research of the optimal reinsurance and investment problems is of great practical significance, which the aim is to maximize the expected exponential utility of the terminal wealth.In chapter 1, we simply introduce the research background and the present situation of the optimal reinsurance and investment.In chapter 2, we introduce the basic knowledge of the classical risk model, risk jump diffusion model, the proportional reinsurance and excess of loss reinsurance.In chapter 3, we consider the problem of optimal excess-of-loss reinsurance and investment strategies under the Ornstein-Uhlenbeck process for an insurer, we assume that the aim of the insurer is to maximize the expected exponential utility of the terminal wealth, and the stochastic control problem of insurer under different strategy is considered:(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 expres-sions for optimal strategies and optimal value functions for the conditions are derived by using stochastic dynamic approach. Finally, some examples are given to show the impact of relevant parameters on the optimal strategies.In chapter 4, we consider the problem of optimal excess-of-loss reinsurance and investment strategies under the jump-diffusion risk process for an insurer whose target is to maximize the expected exponential utility of the terminal wealth. We assume the insurer can invest in a risk-free market and a risky market, the instantaneous return rate of the risky asset is driven by Geometric Levy process. By applying stochastic control theory, the explicit expressions of the optimal investment strategy and the optimal value function are obtained. Finally, some numerical examples are given to show the impact of relevant parameters on the optimal strategies.In chapter 5, we consider a robust optimal reinsurance and investment problem under Ornstein-Uhlenbeck process for an Ambiguity-Averse Insurer. The surplus process of the insurer is assumed to follow a Brownian motion with drift. The financial market consists of one risk-free asset and one risky asset whose price process satisfies Ornstein-Uhlenbeck model. By adopting the stochastic dynamic programming approach, the explict expressions for the maximal exponential utility and the corresponding optimal policies are obtained under uncertainty of the surplus and investment.