英文标题：
《Multivariate Stop loss Mixed Erlang Reinsurance risk: Aggregation,
Capital allocation and Default risk》
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作者：
Gildas Ratovomirija
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最新提交年份：
2015
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英文摘要：
In this paper, we address the aggregation of dependent stop loss reinsurance risks where the dependence among the ceding insurer(s) risks is governed by the Sarmanov distribution and each individual risk belongs to the class of Erlang mixtures. We investigate the effects of the ceding insurer(s) risk dependencies on the reinsurer risk profile by deriving a closed formula for the distribution function of the aggregated stop loss reinsurance risk. Furthermore, diversification effects from aggregating reinsurance risks are examined by deriving a closed expression for the risk capital needed for the whole portfolio of the reinsurer and also the allocated risk capital for each business unit under the TVaR capital allocation principle. Moreover, given the risk capital that the reinsurer holds, we express the default probability of the reinsurer analytically. In case the reinsurer is in default, we determine analytical expressions for the amount of the aggregate reinsured unpaid losses and the unpaid losses of each reinsured line of business of the ceding insurer(s). These results are illustrated by numerical examples.
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中文摘要：
在本文中，我们讨论了相依止损再保险风险的集合，其中分出保险人风险之间的相依性由萨马诺夫分布决定，每个风险都属于Erlang混合类。我们通过推导综合止损再保险风险分布函数的闭合公式，研究了分出保险人风险依赖性对再保险人风险状况的影响。此外，通过推导再保险人整个投资组合所需的风险资本的封闭表达式，以及根据TVaR资本分配原则为每个业务单元分配的风险资本，来检验聚合再保险风险的多元化效应。此外，考虑到再保险人持有的风险资本，我们解析地表达了再保险人的违约概率。如果再保险人违约，我们确定再保险未付损失总额和再保险分出保险人各再保险业务线未付损失的分析表达式。数值算例说明了这些结果。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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