几类风险模型的最优分红问题研究

The optimal dividend problem is one of the interesting problems in insurance actuarial science. In this project we will consider the optimal dividend problems in several risk models under hybrid dividend strategy and a combinational form of threshold strategy and impluse strategy respectively. We will use the methods of probability theory, stochastic process, stochastic control, martingale theory and renewal theory to investigate the optimal dividend problems. We will first consider the dividend problems in Levy risk models and dependent risk models under hybrid dividend strategy and give their optimal dividend strategies. Then we will investigate the optimal dividend problems in Levy risk models and dependent risk models under a combinational form of threshold strategy and impluse strategy and their optimal dividend strategies will also be given. These problems not only have applications for financial and insurance institutions, but also are frontier problems for the insurance actuarial science.

最优分红问题是保险精算学研究的热点问题之一。本项目计划研究几类风险模型在混合分红策略和组合分红策略下的最优分红问题，我们主要利用概率论、随机过程、随机控制、鞅论及更新理论中的方法和技巧进行探讨。首先我们将考虑Levy风险模型和相依风险模型在混合分红策略下的最优分红问题并分别给出其最优分红策略；其次我们将研究Levy风险模型和相依风险模型在组合分红策略下的最优分红问题，给出相应的最优分红策略。这些问题不仅在金融保险机构中有应用背景，而且它们对保险精算理论本身而言，也是具有很大挑战的前沿问题。

本项目致力于研究几类风险模型的最优分红问题。该项目主要从以下两个方面研究：一是研究扩散及levy风险模型中的最优分红策略及相关问题，如随机利率下期望效用分红支付的最优比例再保险分红策略，最小破产概率，模糊厌恶下的最优投资再保险策略；二是讨论levy相依风险模型中的最优分红问题，如研究随机利率下的最优再保险混合分红策略。此外还得到了倒向随机微分方程的解。这些问题不仅可为金融保险机构科学运营提供理论支持，而且它们对于保险精算理论本身而言，也是具有很大挑战的前沿问题。