Research On Optimal Investment-reinsurance Strategy

In market economy,insurance companies have indispensable roles that provide finan-cial protection to individuals and collectives and gain premiums in the process of selling insurance policies to consumers.In order to get greater benefits,insurers always choose to invest the gained money in financial market such as buying stocks,bonds and so on.However,due to the constrained capital scale,sometimes insurers need to ceded a certain of premiums to reinsurers in exchange of the commitment of sharing the risk.A common problem emerged in such operation that how to choose the strategy of buying the stocks and purchasing reinsurance.The issue can be summarized as an optimal investment-reinsurance problem.In this paper we will study the problem in a variety of models.The rest of the thesis is organized as follows.(1)In Chapter 2,we investigate the formulation of optimal investment-reinsurance strategy for a general two-piece utility function.By using martigale theory and convex optimization method,we can transform the original dynamic maximization problem into a static optimization problem.The terminal wealth variable can be obtained from the solution to the static problem.After calculating the conditional expectation on it and doing some comparisons,we can get the corresponding optimal strategy.Moreover,some examples about common utility functions are provided.(2)For insurers who manage property insurance,variance premium is much broad-er applicable and more significant.In Chapter 3,we consider the optimal investment-reinsurance problem basing on variance premium.To make our description more realistic,A continuous time Markov chain is used to represent the constantly changing parameters of market which is also called regime-switching model.The optimal strategy under two different risk models are considered.In addition,we also make some constraint on the amount invested in securities market and the allowable shares of reinsurance which has practical benefit for application.(3)In the past work,optimal reinsurance problems axe treated from the insurer's point of view.In literature,little attention has been paid to determining optimal rein-surance from the reinsurer's point of view or the adjoint interests of the insurer and the reinsurer.However,as any reinsurance policy is a mutual agreement between two parties—the insurer and the reinsurer,optimal reinsurance constructed with only one party is somewhat unreasonable.In other words,an optimal reinsurance treaty obtained by taking into account only the interest of any one party may be unacceptable to the other party.Chapter 4 proposes a new paradigm to analyze optimal reinsurance from the perspectives of an insurer and a reinsurer in a Stackelberg game setting.The reinsurer lies in a leader position in the game for his abundant capital and powerful risk resistance capacity,while insurer acts as a follower to go after reinsurer.We will consider the game problem under the object that maximizing expected exponential utility and attempt to find optimal strategies via solving two associated extended HJB equations.(4)Following the previous discussion,another widespread used model:mean-variance model is considered in Chapter 5.As the objective function can not be written as a function of expectation of terminal wealth,the Bellman ' s principle of optimality does not work and HJB equation is not available.We employ the methodology in Bjork and Murgoci[16]to solve the so-called time inconsistent problem.With the aid of two extended HJB equations,the equilibrium strategy can be obtained.We consider two kinds of reinsurance:excess of loss reinsurance and proportional reinsurance in this Chapter.The results and conclusions of this paper enrich the study of optimal investment-reinsurance problem,which may help the insurers and reinsurers analyze and select the relevant investment and reinsurance strategies.