基于时间不一致性偏好与扩散模型的最优分红策略

本文考虑具有时间不一致性偏好的企业管理者的最优分红策略.假定企业盈余资金由一般扩散模型描述,管理者的偏好由准双曲贴现函数刻画,目标是最大化破产前的累积红利现值.基于管理者对自己未来偏好的认识,分别考虑幼稚型和成熟型管理者的最优分红策略.首先利用随机最优控制方法,得到了两类管理者优化问题的HJB方程及验证定理.然后以常系数扩散模型为例,得到幼稚型与成熟型管理者的最优分红策略及最优值函数的解析式,并对分红策略进行了敏感性分析.结果表明常系数扩散模型下具有时间不一致性偏好的管理者倾向于提前分红,其中成熟型管理者比幼稚型管理者更倾向于发放红利;此外,通过对幼稚型与成熟型管理者施加合适的破产惩罚,可使得幼稚型与成熟型管理者的最优策略与无破产惩罚的时间一致性偏好管理者的最优策略相同.

Optimal dividend strategy for a diffusion model with time-inconsistent preferences

This paper considers the optimal dividend problem in the presence of time-inconsistent preferences. Suppose that the company's surplus follows a general diffusion process, managers' preferences are depicted by the quasi-hyperbolic discount function, and the objective is to maximize the cumulative present value of dividend payments until ruin. Depending on the manager's forecast about his/her own future preferences, we consider the optimal dividend problem for a naive manager and a sophisticated manager. Firstly, we derive the Hamilton-Jacobi-Bellman (HJB) equations and verification theorems for the two managers' problems by using the stochastic optimal control approach. Then, when the un-controlled surplus process is a Brownian motion with drift, we derive the explicit expressions of optimal dividend strategies and optimal value functions for the two managers, and present some sensitivity analysis of the optimal dividend strategies. Our results show that when the un-controlled surplus process is a Brownian motion with drift, managers with time-inconsistent preferences tend to pay out dividend earlier than their time-consistent counterpart, the sophisticated manager is more inclined to pay out dividends than the naive manager, and with proper punishments on the naive manager and the sophisticated managers, the two managers' strategies can coincide with that of the time-consistent manager.