Analysis of ruin measures for the classical compound Poisson risk model with dependence
Analysis of ruin measures for the classical compound Poisson risk model with dependence
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DOI：
10.1080/03461230903211992
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发表时间：
2010-08
影响因子：
1.8
通讯作者：
Hélène Cossette;É. Marceau;Fouad Marri
中科院分区：
文献类型：
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作者：
Hélène Cossette;É. Marceau;Fouad Marri
本文考虑了经典复合泊松风险模型的一个扩展。历史上，人们一直认为索赔金额和索赔间隔到达时间是相互独立的。在这篇文章中，通过法利-冈贝尔-摩根斯特恩关系引入了索赔金额与索赔时间之间的依赖关系结构。在此框架下，我们导出了Gerber-Shiu折现罚函数的积分微分方程和拉普拉斯变换。对于具有指数分布的索赔金额，得到了破产时亏损一般函数贴现值的LT的显式表达式。
In this paper, we consider an extension to the classical compound Poisson risk model. Historically, it has been assumed that the claim amounts and claim inter-arrival times are independent. In this contribution, a dependence structure between the claim amount and the interclaim time is introduced through a Farlie–Gumbel–Morgenstern copula. In this framework, we derive the integro-differential equation and the Laplace transform (LT) of the Gerber–Shiu discounted penalty function. An explicit expression for the LT of the discounted value of a general function of the deficit at ruin is obtained for claim amounts having an exponential distribution.