Risk Measures and Multivariate Extensions of Breiman's Theorem
Risk Measures and Multivariate Extensions of Breiman's Theorem
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DOI：
10.1017/s0021900200009141
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发表时间：
2012-06
期刊：
影响因子：
--
通讯作者：
Anne-Laure Fougères;Cécile Mercadier
中科院分区：
文献类型：
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作者：
Anne-Laure Fougères;Cécile Mercadier
由于偿付能力资本要求的要求，保险风险建模是一项越来越受到关注的任务。破产概率已成为评估监管资本的标准风险指标。本文主要研究夜间视界的离散时间模型。几个结果是可用的，在文献允许校准破产概率的手段，个人索赔金额的尾部概率的总和。本文的目的是得到这些概率在多变量规则变化下的渐近性，更确切地说，是由Breiman定理的扩展导出它们。因此，我们展示了破产概率允许可计算等价物的新情况。结果也是根据风险价值得出的。
Modeling insurance risks is a task that received an increasing attention because of Solvency Capital Requirements. The ruin probability has become a standard risk measure to assess regulatory capital. In this paper we focus on discrete time models for nite time horizon. Several results are available in the literature allowing to calibrate the ruin probability by means of the sum of the tail probabilities of individual claim amounts. The aim of this work is to obtain asymptotics for such probabilities under multivariate regularly variation and, more precisely, to derive them from Breiman's Theorem extensions. We thus exhibit new situations where the ruin probability admits computable equivalents. Consequences are also derived in terms of the Value-at-Risk.