通胀不确定下带有提取约束的最优股利分配  

Optimal Dividend Distribution under Drawdown Constraints in Inflation Uncertainty

作　　者：王康[1] 梁勇[1] WANG Kang;LIANG Yong(School of Mathematics-Physics and Finance,Anhui Polytechnic University,Wuhu 241000,Anhui,China)

机构地区：[1]安徽工程大学数理与金融学院,安徽芜湖241000

出　　处：《合肥学院学报（综合版）》2024年第2期37-45,共9页Journal of Hefei University：Comprehensive ED

基　　金：安徽省高端装备智能控制国际联合研究中心开放基金“G-布朗运动驱动的随机神经网络指数稳定性研究”(IRICHE-05)。

摘　　要：利用通胀对公司的财富过程折现,并采用常相对风险厌恶效用函数,建立相应的随机模型以及最优股利分配模型,得出相应的Hamilton-Jacobi-Bellman变分不等式作为一个非线性自由边界问题,并通过勒让德变换进行求解。最终得出的结论是最优股利率是公司当前盈余和历史最高股利率的函数,此外,随着通货膨胀率越大,股东财富价值也会越小。Using inflation to discount the company´s wealth process and use Constant Relative Risk Aversion utility function, we establish the corresponding stochastic model and optimal dividend distri⁃ bution model, and give the corresponding Hamilton-Jacobi-Bellman variational inequality as a nonlin⁃ ear, free-boundary problem and solve it through the Legendre transform.The final conclusion is that the optimal dividend rate is a function of the company’s current surplus and the historical peak of the dividend rate. In addition, the greater the inflation rate, the smaller the value of shareholders´ wealth will be.

关 键 词：通货膨胀 最优股利分配 CRRA效用函数 HJB方程 勒让德变换 

分 类 号：O175.14[理学—数学]