跳扩散下保险公司投资和再保险策略研究

发布时间：2018-01-31 01:00

本文关键词： 比例再保险多维跳扩散 HJB方程 Lagrange对偶定理违约　出处：《上海师范大学》2014年硕士论文　论文类型：学位论文

【摘要】：在金融机构中,保险公司发挥了越来越重要的作用.保险公司在帮助投保人规避风险的同时也实现了自身的盈利,增加了金融市场的效率,在国民经济建设及社会保障中起到了举足轻重的作用.保险公司的管理层如何有效地运营资本,规避风险,保障金融系统的稳定运行成为一个重要课题.本文考虑多维跳扩散市场下保险公司的最优控制策略问题.保险公司的管理层通过选择控制策略,如再保险比例、投资策略来实现公司价值最大化、风险最小化等. 本文首先在第一章介绍了保险公司投资跳扩散市场和购买比例再保险的最优控制策略问题的主要研究方法和现状,第二章介绍了本文模型所用到的基本预备知识.在第三章中,保险公司通过购买比例再保险来分散一部分风险,同时又将资产投资于资本市场,并且风险资产采用多维跳扩散模型.目标是选择最优的再保险比例和投资策略,使得在某一固定的时刻公司价值达到最大,并求出相应的值函数.本文首先将多维问题转化为一维问题,然后利用动态规划原理求得最优问题的HJB方程,最终求得最优的再保险比例和投资策略.并通过实例进行分析. 在第四章中,保险公司购买比例再保险,并将资产投资十多维跳扩散资本市场,目标是在保险公司期望终值财富为定值时,选择最优的投资和比例再保险策略使终期方差最小,也就是风险最小,并且求得最小方差.为解决这个问题,利用LagrangeX时偶方法,把均值-方差问题看成带等式约束的最优控制问题,然后引入Lagrange乘子把原问题转化为一个不带等式约束的最优控制问题,从而可以利用动态规划的方法进行求解,最后关于Lagrange乘子求最优便得到原问题的解.最后就得到的结果进行相关分析讨论. 在第五章中,保险公司购买比例再保险,并将资产投资于带有跳扩散的资本市场,这里考虑再保险公司存在违约的可能,那么保险公司在t时刻的盈余过程就需要从两种情况来考虑,即t时刻之前违约和t时刻之后违约,之后用示性函数将两种情况写为一个随机微分方程.目标是选择最优的再保险比例和投资策略,使得在某一固定的时刻公司价值达到最大,并求出相应的值函数.求解过程采用第二章中的方法. 在第六章的结论与展望中,给出了本文还存在的不足和今后要深入研究的方向.
[Abstract]:Insurance companies play a more and more important role in financial institutions. Insurance companies help policy holders avoid risks, but also achieve their own profits, increasing the efficiency of the financial market. It plays an important role in national economic construction and social security. How the management of insurance companies operate capital effectively to avoid risks. To ensure the stable operation of the financial system has become an important issue. This paper considers the optimal control strategy of insurance companies in the multi-dimensional jump diffusion market. The management of insurance companies choose control strategies such as reinsurance ratio. Investment strategy to maximize the value of the company, risk minimization and so on. In the first chapter, this paper introduces the main research methods and current situation of the optimal control strategy of investment jump diffusion market and purchasing proportional reinsurance of insurance companies. The second chapter introduces the basic preparatory knowledge used in this model. In the third chapter, the insurance company distributes part of the risk by purchasing proportional reinsurance, while investing assets in the capital market. And risk assets use multi-dimensional jump diffusion model, the goal is to select the optimal reinsurance ratio and investment strategy, so that the company value at a fixed time to achieve the maximum. In this paper, the multidimensional problem is first transformed into a one-dimensional problem, and then the HJB equation of the optimal problem is obtained by using the dynamic programming principle. Finally, the optimal reinsurance ratio and investment strategy are obtained. In Chapter 4th, insurance companies buy proportional reinsurance, and invest their assets in ten dimensional jumps to diffuse capital markets, with the goal being when the insurance company expects the ultimate value of wealth to be fixed. In order to solve this problem, the optimal investment and proportional reinsurance strategies are chosen to minimize the terminal variance, that is, the minimum risk, and to obtain the minimum variance. In order to solve this problem, the LagrangeX time-even method is used to solve this problem. The mean-variance problem is regarded as an optimal control problem with equality constraints, and then the Lagrange multiplier is introduced to transform the original problem into an optimal control problem without equality constraints. Finally, the solution of the original problem can be obtained by using the method of dynamic programming. Finally, the solution of the original problem can be obtained by using the Lagrange multiplier. Finally, the correlation analysis and discussion of the obtained results are carried out. In Chapter 5th, insurance companies buy proportional reinsurance and invest their assets in capital markets with a jump diffusion, considering the possibility of reinsurance companies defaulting. Then the earnings process of the insurance company in the t moment needs to be considered from two situations, namely, the default before the t moment and the default after the t moment. The objective is to select the optimal reinsurance ratio and investment strategy so as to maximize the value of the company at a fixed time. The corresponding value function is obtained, and the method in the second chapter is used to solve the problem. In the conclusion and prospect of Chapter 6th, the deficiency of this paper and the direction of further research are given.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F840.31

【参考文献】