保费和索赔到达率与余额相依的最优有界分红率问题

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。

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

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.