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保费率和索赔到达率与余额相依模型的最优有界分红率问题

刘雪1,李静伟2,刘国欣1   

  1. 1. 河北工业大学理学院
    2.
  • 收稿日期:2018-12-10 发布日期:2019-04-22
  • 通讯作者: 刘国欣
  • 基金资助:
    山西省高校人文社科重点研究基地项目

Optimal Dividend Strategies for Surplus-Dependent Premiums and Surplus-Dependent Claim Arrivals rates: The Cases of Bounded Dividend rates

  • Received:2018-12-10 Published:2019-04-22
  • Contact: GuoXin Liu

摘要: 本文研究了保费率和索赔到达率与余额相依模型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, 我们给出了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(测度值DPE), 并且给出了验证定理的证明. 最后, 我们讨论了测度值DPE和QVI之间的关系, 并且证明了最优分红策略为具有带状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, 带状结构

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 (measure-valued DPE). Finally, We discuss the relationship between the measure-valued DPE and the 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