Ruin probabilities and aggregrate claims distributions for shot noise Cox processes
Ruin probabilities and aggregrate claims distributions for shot noise Cox processes
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DOI：
10.1080/03461230600630395
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发表时间：
2006-03
影响因子：
1.8
通讯作者：
H. Albrecher;Søren Asmussen c
中科院分区：
文献类型：
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作者：
H. Albrecher;Søren Asmussen c
我们考虑了一个风险过程Rt，其中索赔到达过程是齐次Poisson过程和具有Poisson散粒噪声强度过程的Cox过程的叠加，捕捉了外部事件导致索赔强度突然增加的影响。在这些假设条件下，研究了总索赔额的分布。对于轻尾和重尾索赔规模分布，分别给出了无限时间和有限时间破产概率的渐近估计。此外，我们还讨论了将该模型扩展为根据过去的索赔经验动态调整的自适应保费规则。
We consider a risk process R t where the claim arrival process is a superposition of a homogeneous Poisson process and a Cox process with a Poisson shot noise intensity process, capturing the effect of sudden increases of the claim intensity due to external events. The distribution of the aggregate claim size is investigated under these assumptions. For both light-tailed and heavy-tailed claim size distributions, asymptotic estimates for infinite-time and finite-time ruin probabilities are derived. Moreover, we discuss an extension of the model to an adaptive premium rule that is dynamically adjusted according to past claims experience.