Prediction in a Poisson cluster model
Prediction in a Poisson cluster model
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DOI：
10.1239/jap/1276784896
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发表时间：
2010-06
影响因子：
1
通讯作者：
Muneya Matsui;T. Mikosch
中科院分区：
文献类型：
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作者：
Muneya Matsui;T. Mikosch
我们考虑了一个泊松集群模型，该模型的动机是保险申请。在每个索赔到达时间，由齐次泊松过程的点建模，我们启动一个集群过程，代表投资组合中索赔到达触发的付款数量或金额。簇过程是L过程或截断复合泊松过程。给出在有限时间间隔内观察到的过程，我们考虑未来时间间隔内付款数量和金额的期望值。我们还给出了在此预测过程中遇到的误差的界。
We consider a Poisson cluster model, motivated by insurance applications. At each claim arrival time, modeled by the point of a homogeneous Poisson process, we start a cluster process which represents the number or amount of payments triggered by the arrival of a claim in a portfolio. The cluster process is a Lévy or truncated compound Poisson process. Given the observations of the process over a finite interval, we consider the expected value of the number and amount of payments in a future time interval. We also give bounds for the error encountered in this prediction procedure.