复合二项对偶模型中的周期性分红问题

发布时间：2018-07-05 09:39

本文选题：对偶模型 + 周期性分红　；参考：《湘潭大学》2017年硕士论文

【摘要】：该文主要在有界红利率的条件下讨论复合二项对偶模型的周期性分红问题。通过对值函数进行变换,得到了最优红利策略的一些性质,并且证明了最优值函数是一个HJB方程的唯一解。从而得到了最优策略和最优值函数的一个简单计算方法。根据最优红利策略的一些性质,该文还得到了最优值函数的可无限逼近的上界和下界。最后提供一些数值计算实例来说明该算法。该文主要内容如下:第二章介绍了基本模型和给出最优控制问题的一个严格数学表达。第三章给出了最优值函数的HJB方程,得到了最优分红策略的一些性质。第四章通过最优红利策略的一些性质得到了最优值函数的可无限逼近的上界和下界,并通过几个数值计算实例来说明该算法。
[Abstract]:In this paper, we discuss the periodic dividend of compound binomial duality model under the condition of bounded red interest rate. By transforming the value function, some properties of the optimal dividend strategy are obtained, and it is proved that the optimal value function is the unique solution of a HJB equation. A simple calculation method of optimal strategy and optimal value function is obtained. According to some properties of optimal dividend strategy, the upper bound and lower bound of infinite approximation of optimal value function are also obtained. Finally, some numerical examples are provided to illustrate the algorithm. The main contents of this paper are as follows: in chapter 2, we introduce the basic model and give a strict mathematical representation of the optimal control problem. In chapter 3, we give the HJB equation of the optimal value function and obtain some properties of the optimal dividend policy. In chapter 4, we obtain the upper bound and lower bound of infinite approximation of optimal value function by some properties of optimal dividend strategy, and illustrate the algorithm by several numerical examples.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224

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