带干扰与注资的二维对偶模型限制分红问题  

Restricted Dividends in the Two-dimension Dual Model under Diffusion and Capital Injection

作　　者：权俊亮 胡华 QUAN Junliang;HU Hua(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China)

机构地区：[1]宁夏大学数学统计学院,银川750021

出　　处：《华南师范大学学报（自然科学版）》2020年第6期97-102,共6页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11361044);宁夏回族自治区自然科学基金项目(2019AAC03038)。

摘　　要：研究了带干扰二维对偶模型中再注资且分红贴现利率变化的最优分红问题;运用随机控制中HJB方程,证明了最优分红策略是阈值策略,并且得到了累积分红折现期望值函数所满足的积分-微分方程,并用此方程得到收益服从指数分布时值函数的显性表达式.The problem of optimal dividend payment in the two-dimension dual model with diffusion under capital injection and varying dividend discount rates was discussed.The HJB equation in the stochastic control model is used to prove that the optimal strategy is a threshold strategy and the integral-differential equation satisfied by the value function of the cumulative dividend discount expectation is obtained,and the explicit expression of the value function is obtained when the benefit obeys an exponential distribution.

关 键 词：对偶模型 阈值策略 HJB方程 限制分红 

分 类 号：O211.67[理学—概率论与数理统计]