保费和索赔到达率与余额相依的最优有界分红率问题

doi:10.15960/j.cnki.issn.1007-6093.2021.01.003

运筹学学报 ›› 2021, Vol. 25 ›› Issue (1): 31-49.doi: 10.15960/j.cnki.issn.1007-6093.2021.01.003

保费和索赔到达率与余额相依的最优有界分红率问题

刘雪¹, 李静伟², 刘国欣¹^,*()

1. 河北工业大学理学院, 天津 300401
2. 河北工业大学经济管理学院, 天津 300401

收稿日期:2018-12-10 出版日期:2021-03-15 发布日期:2021-03-05
通讯作者: 刘国欣 E-mail:gxliu@hebut.edu.cn
作者简介:刘国欣 E-mail: gxliu@hebut.edu.cn
基金资助:
国家自然科学基金(11471218)

Optimal dividend strategies for surplus-dependent premiums and surplus-dependent claim arrivals rates: the cases of bounded dividend rates

Xue LIU¹, Jingwei LI², Guoxin LIU¹^,*()

1. School of Science, Hebei University of Technology, Tianjin 300401, China
2. School of Economics and Management, Hebei University of Technology, Tianjin 300401, China

Received:2018-12-10 Online:2021-03-15 Published:2021-03-05
Contact: Guoxin LIU E-mail:gxliu@hebut.edu.cn

摘要/Abstract

摘要：

研究保费和索赔到达率与余额相依的最优有界分红问题，目标是最大化破产前的累积期望折现分红。首先，给出一个策略是平稳马氏策略的充分必要条件，运用测度值生成元的理论得到测度值动态规划方程（DPE），并且给出了验证定理的证明。最后，讨论了测度值DPE和相应拟变分不等式（QVI）之间的关系，并且证明了最优分红策略为具有波段结构的平稳马氏策略。

关键词: 最优分红问题, PDMP, 测度值DPE, 马氏策略, 波段结构

Abstract:

In this paper, we consider the optimal dividend problem with bounded dividend rate for the risk model with surplus-dependent premiums and surplus-dependent claim arrivals. The objective is to maximize the expected cumulative discounted dividends payment up to the time of ruin. Firstly, we prove that the necessary and sufficient condition for a strategy to be a stationary Markov strategy. Using the the theory of measure-valued generators, we derive the associated measure-valued dynamic programming equation (DPE). Finally, we discuss the relationship between the measure-valued DPE and the corresponding quasi-varational inequalities (QVI), and show that the optimal dividend strategy is a stationary Markov strategy with a band structure.

Key words: optimal dividend problem, PDMP, measure-valued DPE, Markov strategy, band structure

中图分类号:

O211

刘雪, 李静伟, 刘国欣. 保费和索赔到达率与余额相依的最优有界分红率问题[J]. 运筹学学报, 2021, 25(1): 31-49.

Xue LIU, Jingwei LI, Guoxin LIU. Optimal dividend strategies for surplus-dependent premiums and surplus-dependent claim arrivals rates: the cases of bounded dividend rates[J]. Operations Research Transactions, 2021, 25(1): 31-49.

参考文献 12

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保费和索赔到达率与余额相依的最优有界分红率问题

Optimal dividend strategies for surplus-dependent premiums and surplus-dependent claim arrivals rates: the cases of bounded dividend rates

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