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

作　　者：刘雪 李静伟 刘国欣[1] LIU Xue;LI Jingwei;LIU Guoxin(School of Science,Hebei University of Technology,Tianjin 300401,China;School of Economics and Management,Hebei University of Technology,Tianjin 300401,China)

机构地区：[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

出　　处：《运筹学学报》2021年第1期31-49,共19页Operations Research Transactions

基　　金：国家自然科学基金(No.11471218)。

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。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.

关 键 词：最优分红问题 PDMP 测度值DPE 马氏策略 波段结构 

分 类 号：O211[理学—概率论与数理统计]