结合MIPP型跳的破产理论

中文摘要 AI 辅助

本文研究了当索赔服从多重迭代泊松过程（Multiply Iterated Poisson Process，MIPP）时，保险公司盈余过程的破产概率。该设定扩展了经典的Cramer-Lundberg模型，允许索赔成批到达，特别适用于建模灾难性保险损失。主要贡献是推导了终极破产的显式准则，表明破产概率主要由跳强度参数和迭代次数决定。此外，本文建立了生存概率和破产概率的积分-微分方程，并计算了它们的拉普拉斯变换；这些变换通过递归公式关联，该公式联系了连续迭代水平下的破产概率。本文还引入了一种Cramer-Lundberg型近似，提供了破产概率的渐近表达式以及Lundberg型不等式。本文给出了数值例子，包括与经典模型的比较，以验证理论结果并凸显索赔成批到达对保险公司破产风险的影响。

英文摘要

The paper studies the ruin probability for an insurer's surplus process when claim arrivals are governed by a Multiply Iterated Poisson Process (MIPP). This framework generalizes the classical Cramér-Lundberg model by permitting claims to arrive in clusters, which makes it well suited for representing catastrophic insurance events. The main result is the development of explicit conditions for ultimate ruin, demonstrating that the ruin probability is driven chiefly by the jump intensity and the number of iterations. In addition, we derive integro-differential equations for both survival and ruin probabilities and obtain their Laplace transforms. These transforms are connected through recursive relations that tie ruin probabilities at successive iteration levels. We further propose a Cramér-Lundberg-type approximation, yielding asymptotic formulas for ruin probabilities together with a Lundberg-style bound. Finally, numerical experiments - along with comparisons to the classical model - are included to support the theory and to illustrate how claim clustering affects an insurer's likelihood of ruin.

发表机构

• Yiwu Industrial & Commercial College（义乌工商学院）
• Xi’an Jiaotong Liverpool University（西交利物浦大学）

机构由 AI 辅助整理，请以论文原文为准。