最优再保险问题是保险精算研究的一个热点问题，现有的大部分关于该问题的研究是从保险人最优的角度出发的，然而由于保险人和再保险人的利益是不一致的，保险人最优的再保险策略，未必是再保险人的最优策略，甚至该策略再保险人可能都不能接受。所以，从保险人和再保险人双方利益出发设计最优再保险准则更有意义。近年来，一些学者从保险人风险和再保险人风险之和最小化来设计最优化准则，但这一准则下的策略，仍未必能同时被保险人和再保险人所接受。本项目提出一种新的准则，即在原有优化准则下增加参加再保险后保险人和再保险人的效用都不降低的限制。在这一限制下获得的最优再保险策略能确保保险人和再保险人在参加再保险后财富的效用增加，故更易被保险人和再保险人接受。课题将研究在这一限制下成数再保险、停止损失再保险的最优再保险参数确定问题，以及在效用限制下一般情形的最优再保险表达式，并研究考虑投资分红等情形下效用限制的最优再保险问题。

The optimal reinsurance problem is a hot issue of actuarial study, most of the existing studies on this issue only consider the interest of an insurance company. However, an optimal reinsurance treaty for an insurer might not be optimal for a reinsurer and it might not be acceptable for a reinsurer. It is more interesting and practical to design the optimal reinsurance contract that is beneficial to both an insurer and reinsurer. In recent years, some scholars design the optimization guidelines for minimizing the total risk of both the insurer and the reinsurer, but the strategy under this guideline may not be still acceptable by both the insurer and the reinsurer. We will propose a new criterion —the utility constraints for both the insurer and the reinsurer. The optimal reinsurance strategy obtained under this restriction can ensure that the insurer and reinsurer increase the utility of wealth after participating reinsurance, so it is easier to accept by both the insurer and the reinsurer. We will study the optimal reinsurance parameters of quota share reinsurance and stop loss reinsurance under this restriction, and the optimal reinsurance expression under the utility constraints. We will also study the optimal reinsurance problem of utility constraints under investment and dividend.