重尾条件下 Lévy 驱动的保险风险模型中的多元破产
Multivariate Ruin in Lévy-driven Insurance Risk Models under Heavy Tails
查看机构详情
- Singapore University of Technology and Design（新加坡科技设计大学）
- Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）
机构由 AI 辅助整理，请以论文原文为准。
浏览论文内容
中文总结 AI 辅助
本文针对重尾索赔下多业务线保险公司的有限时间破产问题，利用多元Lévy过程与子锥正则变化建模，给出了破产概率的精确缩放率及极限行为，并通过模拟验证。
中文摘要 AI 辅助
本文研究了一家拥有多条业务线且面临重尾索赔的保险公司在有限时间内的破产问题。该保险公司的索赔金额过程被建模为一个多元递增的 Lévy 过程，并可能伴有波动扰动。相关的破产事件可能涉及单条业务线的失败、多条业务线同时失败，或通过内部转移、再保险或担保安排相关联的业务线组的失败。这些事件具有不同的几何结构，且不必在相同的概率尺度上发生。在不同业务线索赔之间具有渐近尾部独立性的条件下，经典的正则变化理论赋予多线失败事件的极限概率为零，因此无法识别破产概率或相应的偿付能力资本要求。通过使用多元 Lévy 过程对累积索赔进行建模，并在正象限的子锥嵌套序列上使用正则变化来建模跨业务线的依赖性，我们提供了破产概率的精确缩放率及其极限行为。此外，本文还针对独立业务线、独立索赔的共同到达、高斯 copula 依赖索赔、Marshall-Olkin 依赖索赔以及二分保险网络等示例给出了显式计算。最后，我们使用蒙特卡洛模拟来支持我们的理论发现。
英文摘要
The paper studies finite-horizon ruin for an insurance company with several lines of business admitting heavy-tailed claims. The claim amount process of the insurance company is modeled as a multivariate increasing Lévy process possibly perturbed with fluctuations. A relevant insolvency event may involve the failure of a single line, of several lines at once, or of groups of lines linked through internal transfers, reinsurance, or a guarantee arrangement. These events have different geometries and need not occur on the same probability scale. Under asymptotic tail independence among claims from different lines, classical regular variation assigns zero limiting probability to a multi-line failure and is therefore unable to identify either the ruin probability or the corresponding solvency capital requirement. Using a multivariate Lévy process to model cumulative claims and regular variation on a nested sequence of subcones of the positive orthant to model dependence across lines, we provide the exact scaling rate of the ruin probability and the limit behavior. Additionally, explicit computations are presented for examples with independent business lines, common arrivals of independent claims, Gaussian copula dependent claims, Marshall-Olkin dependent claims, and bipartite insurance networks. Finally, we use Monte Carlo simulations to support our theoretical findings.
