扩散风险模型最优分红与融资及再保险策略

发布时间：2018-04-25 00:06

本文选题：融资 + 再保险　；参考：《海南师范大学》2017年硕士论文

【摘要】：保险公司都致力于寻找相应的方法来减少公司所承担的风险.其中再保险就是是保险公司减少风险的一种行之有效的办法.但是如果保险公司为了降低风险而签订了再保险协议,那么该公司的收益也会随之降低.近几年,考虑如何通过再保险策略和分红策略来权衡公司的风险和收益成为一个热点问题.本文运用了随机控制理论、最优策略理论和HJB方程等数学理论来研究保险公司的最优再保险、分红和融资的决策.文章中分别考虑了一般的扩散过程和带有负债型扩散过程的比例再保险、有界分红和融资的最优策略.我们的目标是找到使得破产时期望分红与期望融资的差达到最大的策略,并给出相应策略的显示表达式.在一般的扩散模型的基础上,模型的风险和收益的增加或减少可以通过控制比例再保险、有界分红和强制融资策略来达到,当资产到达某个给定值的时候进行分红,使得破产时期望分红与期望融资的差值最大,即找到最优的值函数(期望折现分红减去期望折现融资的最大值).通过求解模型相应的HJB方程,我们得到了最优值函数和最优策略的显示表达式.在带有负债型扩散模型的基础上,考虑了通过控制比例再保险、有界分红和融资权衡模型的风险和收益,当资产到达某个给定值的时候进行分红,使得破产时的期望分红减去期望融资最大,即找到最优的值函数(期望折现分红减去期望折现融资的最大值).考虑了两个不同的最优控制问题,第一个是在不融资情况下,找到相应的值函数和最优策略,第二个是在融资的条件下,找到相应的值函数和最优策略.最后分析两种情况,得到了一般情况下的随机控制问题的解,给出了什么条件下选择融资,什么条件下选择不融资最有利.
[Abstract]:Insurance companies are working to find ways to reduce the risks they take. Reinsurance is an effective way for insurance companies to reduce risk. But if the insurer signs a reinsurance agreement to reduce risk, the company's earnings will also fall. In recent years, it has become a hot issue to consider how to weigh the risk and income of the company through reinsurance strategy and dividend strategy. In this paper, stochastic control theory, optimal strategy theory and HJB equation are used to study the optimal reinsurance, dividend and financing decisions of insurance companies. In this paper, the optimal strategies of general diffusion process and proportional reinsurance with debt diffusion process, bounded dividend and financing are considered respectively. Our goal is to find the strategy to maximize the difference between the expected dividend and the expected financing at the time of bankruptcy, and give the corresponding expression of the strategy. On the basis of the general diffusion model, the increase or decrease of the risk and income of the model can be achieved by controlling proportional reinsurance, bounded dividend and compulsory financing strategy, when the asset reaches a given value. The difference between the expected dividend and the expected financing is the largest in bankruptcy, that is, the optimal value function is found (the expected discount dividend minus the maximum value of the expected discount financing). By solving the corresponding HJB equation of the model, we obtain the display expressions of the optimal value function and the optimal strategy. Based on the debt-type diffusion model, the risks and benefits of the model are considered by controlling proportional reinsurance, bounded dividends and financing, and dividends are paid when the assets reach a given value. When the expected dividend is reduced by the maximum expected financing, the optimal value function is found (the expected discount dividend minus the maximum value of the expected discount financing). Two different optimal control problems are considered. The first is to find the corresponding value function and optimal strategy without financing, and the second is to find the corresponding value function and optimal strategy under the condition of financing. Finally, by analyzing the two kinds of cases, we obtain the solution of the stochastic control problem under general circumstances, and give out the conditions under which financing is chosen and under what conditions it is most advantageous to choose no financing.
【学位授予单位】：海南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F840.31;O211.67

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