带利率的经典风险模型的最优分红问题
The Optimal Dividend Problem in the Classic Risk Model under Force of Interest
摘要: 本文应用策略迭代算法研究带利率的经典风险模型的最优分红问题。为了克服索赔额服从一般分布的最优分红问题求解的困难，引入了与原问题对应的一列辅助优化问题，通过完整求解辅助优化问题，来给出原最优分红问题的最优策略与值函数的新刻画。同时，借助最小非负解理论，给出了求解最优策略和值函数的策略迭代算法。最后，给出了数值例子。
Abstract: The paper applies the policy iteration algorithm to study the optimal dividend problem in the classic risk model under force of interest. To overcome the difficulties in solving the optimal dividend problem when the claim amount follows a general distribution, a sequence of auxiliary optimization problems corresponding to the original problem is introduced. By solving the auxiliary optimization problems completely, a new characterization of the optimal strategy and the value function for the original optimal dividend problem is provided. Additionally, using the theory of minimal non-negative solutions, a policy iteration algorithm for solving the optimal strategy and value function is proposed. Finally, numerical examples are presented.
文章引用：吴微丽. 带利率的经典风险模型的最优分红问题[J]. 应用数学进展, 2025, 14(4): 111-121. https://doi.org/10.12677/aam.2025.144144

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