Optimal Proportional Reinsurance To Maximize The Expected Utility Under Thinning-dependence Structure

Reinsurance optimization is always an important topic in the actuarial science.As we all know an insurance company collects the premium from the insured and is responsible for the risk of the insured.Besides,an insurance company will invest in the financial market and it has to face the risk from the insurance business and the financial business.To transfer some of the risk,insurers usually purchase reinsurance at the expense of making less potential profit Hence,finding an optimal reinsurance strategy to balance the profit and the risk has gained much attention in actuarial liter-ature.In this article,we consider the optimal proportional reinsurance problem in a risk model under the thinning-dependence structure with the reinsurance premium calcu-lated by expected value principle.The thinning dependence assumes that stochastic sources related to claim occurrence are classified into different groups,and that each group may cause a claim in each insurance class with a certain probability.Com-pared with common-shock model,thinning-dependent model is more realistic.It has more parameters to describe the problem and it is easier to adjust and fit in practical applications.Our optimized target is to maximize the expected exponential utility.In Chapter 3,we study the optimal strategies for the thinning-dependent risk model.Firstly,we discuss about the existence and uniqueness of the optimal strategy.Then,by the technique of stochastic control theory and the corresponding Hamilton-Jacobi-Bellman equation we get the explicit expressions for the optimal strategies and value functions.Chapter 4 is devoted to study optimal strategies for the diffusion approxi-mation risk model.General solutions are derived.In Chapter 5,we analyse our results and several numerical examples are provided to show the impacts of parameter on the optimal strategy.From our results,we find the optimal strategies depend not only on the safety loading,time and interest rate,but also on the claim size distributions and the counting processes.Besides,decision maker's attitude towards risk has great impact on the optimal strategies too.