On a risk model with dependence between interclaim arrivals and claim sizes
On a risk model with dependence between interclaim arrivals and claim sizes
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DOI：
10.1080/03461230600992266
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发表时间：
2006-09
影响因子：
1.8
通讯作者：
Mathieu Boudreault;Hélène Cossette;D. Landriault;É. Marceau
中科院分区：
文献类型：
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作者：
Mathieu Boudreault;Hélène Cossette;D. Landriault;É. Marceau
我们考虑了经典复合泊松风险模型的扩展，其中总索赔金额过程的增量是独立的。Albrecher和Teugels（2006）考虑了索赔间时间和后续索赔规模之间的任意依赖结构，并推导了有限和无限时间破产概率的渐近结果。本文考虑了索赔间隔期与后续索赔规模之间的一种特殊的依赖关系结构，并导出了期望折扣惩罚函数所满足的缺陷续期方程。基于破产时间的拉普拉斯变换的复合几何尾表示，我们还得到了一类索赔规模分布的拉普拉斯变换的显式表达式。破产概率是破产时间拉普拉斯变换的一种特殊情况，因此得到了这一特定破产相关量的显式表达式。最后，我们通过比较风险模型中不同依赖结构的伦德伯格系数来衡量它们对破产概率的影响。
We consider an extension to the classical compound Poisson risk model for which the increments of the aggregate claim amount process are independent. In Albrecher and Teugels (2006), an arbitrary dependence structure among the interclaim time and the subsequent claim size expressed through a copula is considered and they derived asymptotic results for both the finite and infinite-time ruin probabilities. In this paper, we consider a particular dependence structure among the interclaim time and the subsequent claim size and we derive the defective renewal equation satisfied by the expected discounted penalty function. Based on the compound geometric tail representation of the Laplace transform of the time to ruin, we also obtain an explicit expression for this Laplace transform for a large class of claim size distributions. The ruin probability being a special case of the Laplace transform of the time to ruin, explicit expressions are therefore obtained for this particular ruin related quantity. Finally, we measure the impact of the various dependence structures in the risk model on the ruin probability via the comparison of their Lundberg coefficients.