绝对破产下一类带干扰复合Poisson-Geometric过程风险模型的分红问题
The Dividend Problems in the Perturbed Poisson-Geometric Processes Risk Model under Absolute Ruin
摘要: 对贷款和随机扰动下索赔次数为复合Poisson-Geometric过程风险模型的分红问题进行研究，得到了绝对破产前分红总量现值的期望、矩母函数以及n阶原点矩满足的积分–微分方程和边界条件，并给出这些积分–微分方程和边界条件的经济学直觉解释，借助confluent hypergeometric函数求出了个体索赔额服从指数分布时的解析表达式。
Abstract: In this paper, we consider the dividend payments problems in a risk model perturbed by diffusion with a constant barrier dividend strategy and debit interest, in which the claim counting process is a compound Poisson-Geometric process. We derive a system of integro-differential equations with boundary conditions satisfied by the moment generating function, the expectation and the nth moment of the cumulative discounted dividend payments until absolute ruin. Furthermore, we give intuitive economic explanations for these integral-differential equations and boundary conditions. Meanwhile, we obtain the explicit expressions when the claim sizes are exponentially distributed by the confluent hypergeometric function.
文章引用：孔梁光, 张申, 陆健云, 陈雪丽, 赵金娥. 绝对破产下一类带干扰复合Poisson-Geometric过程风险模型的分红问题[J]. 应用数学进展, 2026, 15(5): 673-685. https://doi.org/10.12677/aam.2026.155259

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