保险风险模型的破产概率及最优控制策略问题

发布时间：2018-05-13 17:25

本文选题：风险模型 + 破产概率　；参考：《宁夏大学》2014年硕士论文

【摘要】：保险公司在金融机构中发挥着越来越重要的作用,但竞争也日趋激烈,仅仅依靠保险索赔赚取收入的增长方式已经不可持续.与此同时,保险公司拥有大量的现金流,公司管理层如何能有效地运营资本和规避风险尤显重要. 本文建立了三个更加符合市场现状和具有经济意义的模型,通过借助概率与随机分析的思想,构造HJB方程,得到了最优回报函数和相应的最优控制策略.主要工作包括： 1.考虑了变破产下限的单险种风险模型,其破产概率不易求得,但给出了破产概率上界的不等式,此不等式为风险管理提供了有力的工具,对保险公司管理层如何选择其经营策略有一定的指导意义. 2.考虑了保险公司通过连续购买比例再保险控制和管理风险的同时又将公司固定比例的盈余资本投资到风险市场的情况.事实上,在我国,并不允许保险公司将所有盈余资本投资到风险市场.因此,将公司总盈余的固定比例投资于风险市场更具有现实意义. 3.假定资本市场变动与保险公司资本收益变动存在相关性的情况下,利用HJB-变分不等方程求解出最优再保险策略和最小破产概率的显示表达式.最后讨论了受这种相关性影响的一些定量分析.
[Abstract]:Insurance companies play a more and more important role in financial institutions, but the competition is becoming more and more fierce. At the same time, insurance companies have a lot of cash flow, how the management can effectively operate capital and avoid risk is particularly important. In this paper, three models which are more in line with the market situation and have economic significance are established. By using the idea of probability and stochastic analysis, the HJB equation is constructed, and the optimal return function and corresponding optimal control strategy are obtained. The main tasks include: 1. The ruin probability of a single insurance risk model with variable ruin limit is considered. However, the inequality of upper bound of ruin probability is given, which provides a powerful tool for risk management. It has certain guiding significance to how to choose the management strategy of insurance company. 2. This paper considers the situation that the insurance company controls and manages the risk through the continuous purchase proportion reinsurance, and at the same time it invests the company's fixed proportion of surplus capital in the risk market. In fact, insurance companies are not allowed to invest all surplus capital in the risk market in China. Therefore, it is more practical to invest the fixed proportion of total earnings in the risk market. 3. Assuming the correlation between capital market change and capital income change of insurance companies, the optimal reinsurance strategy and the display expression of minimum ruin probability are obtained by using HJB- variational inequality equation. Finally, some quantitative analyses affected by this correlation are discussed.
【学位授予单位】：宁夏大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F840;O232

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