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

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.