Optimal Strategy Of Reinsurance-Investment And Related Problems

For insurance companies to expand their capital size and to enhance their competi-tiveness, investment is an inevitable choice. Meanwhile, an insurer has to further reduce insurance company’s own risk, which makes the reinsurance business be more necessary. This paper mainly discusses the investment-reinsurance problem for the case of constant interest rate and the case of stochastic interest rates, respectively. In addition, some results of DC pension and annuity, insurance pricing are also investigated.The problem of investment and reinsurance under the constant interest rate, is divided into two parts:one is for Brownian motions are independent of each other, the other is for Brownian motions are correlation to each other. Research of the problem of investment and reinsurance under the stochastic interest rate, mainly concentrated on considering the insurance company has a promotional budget. Various of theories and methods are used comprehensively, such as, the optimal control theory, stochastic anal-ysis tools, martingale theory etc.,so that the explicit solutions to most of the problems are obtained. With the help of mathematical software, some numerical simulations are given.The whole content of this dissertation includes six parts, separately divided into five chapters as follows. The first chapter is introduction, which takes up dozens of pages for tracing the history, striving to present the profile of our research field. On the second chapter, the optimal excess of loss reinsurance and investment problems of the constant interest rate are deliberated. On the third chapter, the problem of reinsurance and investment under stochastic interest rates is discussed, which mainly focus on the constant volatility models. On the fourth chapter, reinsurance for one insurer with multiple re-insurers is considered. On the fifth chapter, two related problems of the optimal investment decision and insurance are investigated, the one being related to the DC pension plan and the other one talking about insurance pricing.