复合二项对偶模型中的周期性分红问题  

Optimal Dividend Strategy in Compound Binomial Dual Model with Bounded Dividend Rates and Periodic Dividend Payments

作　　者：游凌云[1] 谭激扬[1] 黎自强[2] 张汉君[1] you Lingyun Tan Jiyang Li Ziqiang Zhang Hanjun(School of Mathematics and Computational Science, Xiangtan University, Hunan Xiangtan 411105 School of Information Engineering, Xiangtan University, Hunan Xiangtan 411105)

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105 [2]湘潭大学信息工程学院,湖南湘潭411105

出　　处：《数学物理学报（A辑）》2017年第4期751-766,共16页Acta Mathematica Scientia

基　　金：国家自然科学基金(61272294;11371301);湖南省自然科学基金(14JJ2069)~~

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.In this paper, we discusses the problem binomial dual model with bounded dividend rates of optimal dividend payment in compound and periodic dividend payments. Through transforming the value function, we obtain some properties of the optimal dividend payment strategy, and show that the optimal value function is the unique solution of a discrete Hamilton- aacobi-Bellman equation. Meanwhile, a simple algorithm is obtained for the optimal strategy and the optimal value function. According to the properties of the optimal dividend strategy, an upper bound and a lower bound of the optimal value function are derived. Numerical examples are presented to illustrate the transformation method.

关 键 词：对偶模型 周期性分红 HJB方程 压缩映射 最优分红策略 

分 类 号：O232[理学—运筹学与控制论]