保险投资组合随机模型中风险控制及优化分红问题的研究

In this project, we intend to use the stochastic process, the stochastic analysis, the stochastic control theory and the mathematical finance to fully study the optimal risk control and optimization of the dividend problems of the risk model, it belongs to a crossover study of risk theory and quantitative finance.Firstly, we study the ruin probability（absolute ruin probability）and expected discounted penalty function of the random risky model through the knowledge of the HJB-equation, the inverter inequality and random analysis theory etc. Secondly, we attend to seek a new dividend policy on the basis of the barrier strategy and the threshold strategy, and solve the optimal dividend strategy by the theory of stochastic processes and stochastic control theory. Finally, we consider the best risk control strategy through stochastic control theory and the method of game theory by optimizing a given objective function, such as expected utility, expected discounted earnings, expected discounted of aggregate dividend payments, value at risk, etc.The project is the latest issue of finance and risk theory, and it's the cross-over of stochastic process, stochastic analysis, stochastic control and mathematical finance, which not only greatly enrich the research in the field, and effectively attract insured as well as the guidence of effective risk investment, but also will promote the development of the stochastic optimal control, mathematical finance and actuarial.

本项目拟利用随机过程、随机分析、随机控制理论以及数理金融的思想充分研究保险投资组合风险模型中最优风险控制及优化分红问题，其属于风险理论与数理金融的交叉研究。首先通过HJB方程、逆变分不等式和随机分析等知识对随机风险模型的破产（绝对破产概率）和期望折现罚金函数展开研究；其次在Barrier分红策略和Threshold分红策略的基础上寻求新的分红策略，并利用随机过程和随机控制理论求解最优分红策略；最后通过优化给定的目标函数，如期望效用，期望折现收益，期望折现分红总量，风险值等，利用随机控制理论和博弈论的方法来寻找最优风险控制策略。该项目研究的问题是金融和风险理论的最新课题，是随机过程、随机分析、随机控制和数理金融的交叉，它不仅极大丰富该领域的研究，并为保险公司吸引投保以及有效进行风险投资有着指导意义，同时也将促进随机最优控制、数理金融和精算等领域的发展。

本项目利用随机过程、随机分析、随机控制理论以及数理金融的思想研究了保险投资组合风险模型中最优风险控制及优化分红问题。首先利用随机过程和随机分析等知识对随机风险模型的破产（绝对破产概率）和期望折现罚金函数展开研究；其次在Barrier分红策略和Threshold分红策略的基础上寻求新的分红策略，并利用随机过程和随机控制理论求解最优分红策略；最后通过优化给定的目标函数，如期望效用，期望折现收益，期望折现分红总量，风险值等。在上述问题的研究过程中我们还利用随机泛函的知识对风险测度进行了研究，并对相依的随机风险模型进行了部分研究，另外对于寿险中人口的分布情况以及相关统计数据的分析方法进行了研究。