复合Poisson 模型带破产罚金的最优分红策略
Optimal Dividend-Penalty Strategy in the Compound Poisson Model
DOI: 10.12677/AAM.2021.1012448, PDF, HTML, 下载: 241  浏览: 321 
作者: 李静伟：天津电子信息职业技术学院经济与管理系，天津
关键词: 复合Poisson 模型；最优分红问题；罚金函数；HJB 方程；Compound Poisson Mode； Optimal Dividend Problem； Gerber-Shiu Function； HJB Equation
摘要: 本文研究了复合 Poisson 模型带破产罚金的最优分红问题。目标是最大化破产时刻之前的累积折现分红和折现罚金之差。首先，本文给出了值函数满足的基本性质。然后，本文推导了值函数满足的 HJB 方程。最后，验证了值函数是HJB方程的解。
Abstract: This paper concers an optimal dividend-penalty problem for the compound Poisson model. The objective is to maximize the difference of the expected cumulative dis-counted penalty payment taken at the moment of ruin and a discounted penalty pay- ment taken at the moment of ruin. Firstly, this paper gives the basic properties of the value function. Then, we derive the HJB equation of the value function. Finally, it is verified that the value function is the solution of the HJB equation.
文章引用：李静伟. 复合Poisson 模型带破产罚金的最优分红策略[J]. 应用数学进展, 2021, 10(12): 4218-4226. https://doi.org/10.12677/AAM.2021.1012448

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