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运筹学学报 >

2021 , Vol. 25 >Issue 1: 31 - 49

DOI: https://doi.org/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

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  • 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
刘国欣 E-mail: gxliu@hebut.edu.cn

收稿日期: 2018-12-10

  网络出版日期: 2021-03-05

基金资助

国家自然科学基金(11471218)

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

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  • 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 date: 2018-12-10

  Online published: 2021-03-05

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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

本文引用格式

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

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

参考文献

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