复合二项对偶模型中的周期性分红问题

数学物理学报 ›› 2017, Vol. 37 ›› Issue (4): 751-766.

复合二项对偶模型中的周期性分红问题

游凌云¹, 谭激扬¹, 黎自强², 张汉君¹

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

收稿日期:2016-12-07 修回日期:2017-04-27 出版日期:2017-08-26 发布日期:2017-08-26
作者简介:谭激扬,E-mail:tanjiyang15@163.com
基金资助:
国家自然科学基金（61272294，11371301）和湖南省自然科学基金（14JJ2069）

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

You Lingyun¹, Tan Jiyang¹, Li Ziqiang², Zhang Hanjun¹

1 School of Mathematics and Computational Science, Xiangtan University, Hunan Xiangtan 411105;
2 School of Information Engineering, Xiangtan University, Hunan Xiangtan 411105

Received:2016-12-07 Revised:2017-04-27 Online:2017-08-26 Published:2017-08-26
Supported by:
Supported by the NSFC (61272294, 11371301) and the Hunan Provincial Natural Science Foundation (14JJ2069)

摘要/Abstract

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.

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

Abstract: In this paper, we discusses the problem of optimal dividend payment in compound binomial dual model with bounded dividend rates 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 HamiltonJacobi-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.

Key words: Dual model, Periodic dividend payments, HJB equation, Contraction mapping, Optimal dividend strategy

中图分类号:

O232

游凌云, 谭激扬, 黎自强, 张汉君. 复合二项对偶模型中的周期性分红问题[J]. 数学物理学报, 2017, 37(4): 751-766.

You Lingyun, Tan Jiyang, Li Ziqiang, Zhang Hanjun. Optimal Dividend Strategy in Compound Binomial Dual Model with Bounded Dividend Rates and Periodic Dividend Payments[J]. Acta mathematica scientia,Series A, 2017, 37(4): 751-766.

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