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.
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