保险公司财富优化管理问题研究
发布时间：2019-02-15 18:27
【摘要】：自从Cramer采用随机过程研究破产问题之后,保险公司的财富优化管理问题开始得到了迅速的发展,其理论不仅充实了金融理论,同时也沟通了金融学、保险学与数学之间的关系.对于保险公司来说,最小化破产概率对其发展有着重要的意义,同时最大化公司财富是管理者的优化目标.论文分别建立盈余过程服从泊松跳跃、复合泊松跳跃以及盈余过程是Levy过程的数学模型,运用鞅方法和随机控制方法对所建模型的破产概率、最优再保险问题以及最优投资-再保险问题分别进行研究,得到破产概率、生存概率所满足的方程以及最优投资-再保险策略.主要研究内容如下:(1)假定盈余过程带有泊松跳跃和盈余过程是Levy过程,对保险公司的破产概率进行研究.分别在常利率、随机利率下以及盈余过程具有Markov调制参数时,运用鞅方法和随机控制的方法得到保险公司的破产概率所满足的偏微分方程.(2)假定盈余过程带有泊松跳跃和盈余过程是Levy过程,以最小化破产概率为目标对保险公司的再保险问题进行研究.运用鞅方法和随机控制的方法得到生存概率所满足的偏微分方程.(3)假定盈余过程带有泊松跳跃和盈余过程带有复合泊松跳跃,以最大化终端财富的期望效用为目标,对保险公司的最优投资-再保险问题进行研究.运用随机动态规划的方法得到最大化期望指数效用的最优投资-再保险策略.
[Abstract]:Since Cramer used stochastic process to study bankruptcy problem, the optimal wealth management of insurance companies has developed rapidly. Its theory not only enriches financial theory, but also communicates the relationship among finance, insurance and mathematics. For insurance companies, minimizing bankruptcy probability is of great significance to their development, and maximizing corporate wealth is the optimization goal of managers. In this paper, the mathematical models of surplus process from Poisson jump, composite Poisson jump and surplus process are established respectively. The ruin probability of the model is obtained by using martingale method and stochastic control method. The optimal reinsurance problem and the optimal investment-reinsurance problem are studied, and the ruin probability, the equation of survival probability and the optimal investment-reinsurance strategy are obtained. The main contents are as follows: (1) assuming that the earnings process has Poisson jump and the earnings process is the Levy process, the ruin probability of the insurance company is studied. In the case of constant interest rate, random interest rate and the Markov modulation parameter of the earnings process, By using martingale method and stochastic control method, the partial differential equations satisfied by the ruin probability of the insurance company are obtained. (2) it is assumed that the surplus process is Levy process with Poisson jump and earnings process. Aiming at minimizing bankruptcy probability, the reinsurance problem of insurance company is studied. By using martingale method and stochastic control method, the partial differential equations of survival probability are obtained. (3) assuming that the surplus process has Poisson jump and the earnings process has compound Poisson jump, the goal is to maximize the expected utility of the terminal wealth. This paper studies the optimal investment-reinsurance of insurance companies. The optimal investment-reinsurance strategy for maximizing the expected exponential utility is obtained by using stochastic dynamic programming.
【学位授予单位】：西安工程大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F224;F840.31
本文编号：2423617
[Abstract]:Since Cramer used stochastic process to study bankruptcy problem, the optimal wealth management of insurance companies has developed rapidly. Its theory not only enriches financial theory, but also communicates the relationship among finance, insurance and mathematics. For insurance companies, minimizing bankruptcy probability is of great significance to their development, and maximizing corporate wealth is the optimization goal of managers. In this paper, the mathematical models of surplus process from Poisson jump, composite Poisson jump and surplus process are established respectively. The ruin probability of the model is obtained by using martingale method and stochastic control method. The optimal reinsurance problem and the optimal investment-reinsurance problem are studied, and the ruin probability, the equation of survival probability and the optimal investment-reinsurance strategy are obtained. The main contents are as follows: (1) assuming that the earnings process has Poisson jump and the earnings process is the Levy process, the ruin probability of the insurance company is studied. In the case of constant interest rate, random interest rate and the Markov modulation parameter of the earnings process, By using martingale method and stochastic control method, the partial differential equations satisfied by the ruin probability of the insurance company are obtained. (2) it is assumed that the surplus process is Levy process with Poisson jump and earnings process. Aiming at minimizing bankruptcy probability, the reinsurance problem of insurance company is studied. By using martingale method and stochastic control method, the partial differential equations of survival probability are obtained. (3) assuming that the surplus process has Poisson jump and the earnings process has compound Poisson jump, the goal is to maximize the expected utility of the terminal wealth. This paper studies the optimal investment-reinsurance of insurance companies. The optimal investment-reinsurance strategy for maximizing the expected exponential utility is obtained by using stochastic dynamic programming.
【学位授予单位】：西安工程大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F224;F840.31
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