Operations Research Transactions

   

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

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