随机环境下两类保险公司的最优控制策略问题研究

发布时间：2018-03-04 03:33

本文选题：保险公司　切入点：固定缴费型养老金计划　出处：《清华大学》2016年博士论文　论文类型：学位论文

【摘要】：保险在个人或企业的经济行为中具有重要的意义,能够有助于降低个人的风险。对于保险公司而言,如何有效地管理保费并进行投资决策是一个重要的课题。按照保险风险标的的不同,本文研究非寿险和养老金类保险公司的最优控制策略问题。由于在以往的研究中,保险公司模型和实际具有一定的偏差,并未考虑更为复杂的随机环境以及投资行为。本文针对非寿险和养老金类保险公司建立更为合理接近实际的金融模型,然后运用鞅方法或者动态规划方法进行求解。本文分四部分研究上述问题。第一部分研究在随机利率和随机通货膨胀下保险公司的最优再保险与投资策略。本文首先通过辅助问题将原问题转化成自融资的问题,然后利用动态规划方法得到了CRRA效用下的最优策略。第二部分研究在随机利率下固定缴费型养老金的投资组合问题,考虑了两种优化目标:损失规避和VaR约束。文中通过鞅方法得到了两种优化原则下的最优策略,并进行了对比。第三部分研究了随机利率和随机波动率下固定缴费型养老金的投资组合问题,养老金管理者需要最大化退休时刻财富超出最低生活保障部分的CRRA效用,通过引入辅助过程并利用动态规划方法,本文得到了显式解。第四部分讨论了随机利率和随机回报下固定缴费型养老金的投资管理,养老金管理者需要得到期望-方差准则下的有效边界和有效策略。利用Lagrange对偶理论,本文首先将问题转换成一个单目标的优化问题,然后利用动态规划的方法进行了求解。同时,在每一部分,本文通过蒙特卡洛方法进行数值分析和经济行为分析,讨论参数对最优策略的影响,并检验模型的合理性。上面的问题研究了在随机环境和不同优化准则下保险公司的最优控制策略,需要综合运用随机分析、鞅方法和动态规划方法等方法,同时在非自融资情况下需要将问题进行转化,对其他问题的求解具有启发意义。此外,本文的结论对保险公司的投资行为能够提供有效参考。
[Abstract]:Insurance plays an important role in the economic behavior of individuals or enterprises and can help to reduce personal risk. How to manage insurance premium effectively and make investment decision is an important subject. According to the difference of the subject matter of insurance risk, this paper studies the optimal control strategy of non-life insurance and pension insurance companies. There is a certain deviation between the insurance company model and the practice without considering the more complex random environment and the investment behavior. This paper establishes a more reasonable and close to the actual financial model for the non-life insurance and pension insurance companies. Then we use martingale method or dynamic programming method to solve the problem. This paper is divided into four parts. The first part is to study the optimal reinsurance and investment strategy of insurance companies under stochastic interest rate and stochastic inflation. First of all, the original problem is transformed into a self-financing problem through a supplementary problem. Then the optimal strategy under CRRA utility is obtained by using dynamic programming method. The second part studies the portfolio problem of fixed contributory pension at random interest rate. Two optimization objectives, loss avoidance and VaR constraint, are considered in this paper. In this paper, the optimal strategies under two optimization principles are obtained by martingale method. In the third part, we study the portfolio problem of fixed contributory pension under stochastic interest rate and random volatility. Pension managers need to maximize the CRRA utility of wealth beyond the minimum living security in retirement time. By introducing the auxiliary process and using the dynamic programming method, the explicit solution is obtained in this paper. Part 4th discusses the investment management of fixed contributory pension under stochastic interest rate and stochastic return. Pension managers need to obtain efficient boundaries and effective strategies under the expectation-variance criterion. Using Lagrange duality theory, this paper first transforms the problem into a single objective optimization problem. Then the dynamic programming method is used to solve the problem. At the same time, in each part, the influence of the parameters on the optimal strategy is discussed by using the Monte Carlo method for numerical analysis and economic behavior analysis. The above problem studies the optimal control strategy of insurance companies under random environment and different optimization criteria, and needs to use the methods of stochastic analysis, martingale method and dynamic programming method, etc. At the same time, it is necessary to transform the problem in the case of non-self-financing, which is instructive for solving other problems. In addition, the conclusion of this paper can provide an effective reference for the investment behavior of insurance companies.
【学位授予单位】：清华大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：F224;F840

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