若干带约束的均值-方差最优再保险与投资问题的时间一致性策略

众所周知，再保险与投资是保险人管理风险的两种常用的方法。本项目拟在均值-方差准则下研究最优再保险与投资问题的时间一致性均衡策略。与现有研究不同的是，本项目将考虑下述四种具有实际意义的约束条件：1.比例再保险策略限制在0到1之间且限制卖空风险资产；2.破产约束，即要求保险人的盈余过程恒大于零；3.保险人的风险厌恶系数为状态变量的非负函数；4.保险人仅具有有限的信息处理能力。在确定系数和随机系数模型下，拟利用倒向随机微分方程、完全耦合的正倒向随机微分方程组以及随机滤波等工具得到这四种约束情形下的时间一致性均衡策略，并分析各种约束对均衡策略的影响。我们期望本项目的研究成果可以帮助保险人制定更加合理的风险管理策略。

It is well known that investment and reinsurance are two important ways in which insurers manage risk. This project will study the time-consistent equilibrium strategies for mean-variance optimal reinsurance and investment problems. In contrast to the existing research, we shall consider the following four interesting constraints, respectively: 1. the proportional reinsurance strategy is restricted between 0 and 1 and short-selling the risk asset is prohibited; 2. bankruptcy prohibition, i.e., it is required that the surplus process of the insurer is always positive; 3. the risk aversion of the insurer is given by a general non-negative function of the sate process; 4. the insurer observes the state imperfectly and has limited information-processing capacity. Under models with deterministic coefficients and/or random coefficients, we shall use backward stochastic differential equation, fully coupled forward-backward stochastic differential equation, stochastic filtering, etc. to derive the equilibrium strategies under the above constraints. It is expected that the results of this project will help insurers to make reasonable risk management decisions.