On the probability of ruin in the compound Poisson risk model with potentially delayed claims
On the probability of ruin in the compound Poisson risk model with potentially delayed claims
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DOI：
10.1007/s40065-012-0043-0
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发表时间：
2013-03
影响因子：
1.2
通讯作者：
Jie-hua Xie;W. Zou;Jian-wei Gao
中科院分区：
文献类型：
--
作者：
Jie-hua Xie;W. Zou;Jian-wei Gao
本文研究了具有主索赔和副索赔两类相依索赔的复合Poisson风险模型。附带索赔是由主索赔以一定的概率引发的，并且附带索赔的发生可能会延迟，这取决于相关的主索赔金额。利用Rouché定理，从一个积分微分方程组出发，得到了具有零初始盈余的生存概率和生存概率的拉普拉斯变换.然后，利用拉普拉斯变换，我们得到了一个缺陷更新方程所满足的生存概率。这个方程的解的精确表示是通过一个相关的复合几何分布。对于指数索赔额，我们提出了一个明确的生存概率公式。通过数值例子说明了相依风险模型中模型参数对生存概率的影响。
In this paper, we consider the compound Poisson risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim with a certain probability and the occurrence of a by-claim may be delayed depending on associated main claim amount. Using Rouché’s theorem, both of the survival probability with zero initial surplus and the Laplace transform of the survival probability are obtained from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. An exact representation for the solution of this equation is derived through an associated compound geometric distribution. For exponential claim sizes, we present an explicit formula for the survival probability. We also illustrate the influence of model parameters in the dependent risk model on the survival probability by numerical examples.