ABSTRACT This paper concerns the optimal dividend problem with bounded dividend rate for Sparre Andersen risk model. The analytic characterizations of admissible strategies and Markov strategies are given. We use the measure-valued generator theory to derive a measure-valued dynamic programming equation. The value function is proved to be of locally finite variation along the path, which belongs to the domain of the measure-valued generator. The verification theorem is proved without additional assumptions on the regularity of the value function. Actually, the value function may have jumps. Under certain conditions, the optimal strategy is presented as a Markov strategy with space-time band structure. We present an iterative algorithm to approximate the optimal value function and the optimal dividend strategy. As applications, some numerical examples are given.

中文翻译：

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有界股息率的Sparre Andersen风险模型的最优股息问题

摘要 本文研究了 Sparre Andersen 风险模型的有界股息率的最优股息问题。给出了可接纳策略和马尔可夫策略的解析特征。我们使用测值生成器理论推导出测值动态规划方程。证明该值函数沿路径具有局部有限变化，属于测值生成器的域。验证定理的证明无需额外假设价值函数的正则性。实际上，值函数可能有跳跃。在一定条件下，最优策略表现为具有时空带结构的马尔可夫策略。我们提出了一种迭代算法来逼近最优价值函数和最优股息策略。作为应用程序，