ABSTRACT

This paper investigates a stochastic optimal control problem by the impulse dividend model with stochastic returns. To search for its candidate solution, we propose a series of quasi-variational inequalities (QVI), for which an analytic solution composed of a power series is provided. Moreover, some properties, such as the uniqueness of uncertain parameters and partition points, of the solution are also verified under some conditions. The procedure on how to calculate unknown parameters is also presented. Theorematic analysis verifies that the policy based on the proposed solution is just the optimal dividend policy.

中文翻译：

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具有随机收益的脉冲红利模型的随机最优控制

摘要

本文通过具有随机收益的脉冲红利模型研究了一个随机最优控制问题。为了寻找其候选解，我们提出了一系列拟变分不等式 (QVI)，为此提供了由幂级数组成的解析解。此外，还验证了解的一些性质，如不确定参数和分割点的唯一性。还介绍了如何计算未知参数的过程。理论分析验证了基于所提出解决方案的策略正是最优的分红策略。