Modeling claim exceedances over thresholds

In this paper, we consider a simple risk model and study the occurrences of clusters of threshold exceedances by the individual claims. The statistic used to study the model is the discrete multiple scan statistic. A compound Poisson approximation is established and certain asymptotic results are obtained for both the risk model and a similar in nature financial problem. Finally, we review two typical examples from areas of applied science where the outcomes of this paper may have beneficial impact.