In this paper, we discuss a generalization of the classical compound Poisson model with claim sizes following a compound distribution. As applications, we consider models involving zero-truncated geometric, zero-truncated negative-binomial and zero-truncated binomial batch-claim arrivals. We also provide some ruin-related quantities under the resulting risk models. Finally, through numerical examples, we visualize the behavior of these quantities.

中文翻译：

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索赔规模服从复合分布的经典复合泊松模型的应用

在本文中，我们讨论了索赔规模服从复合分布的经典复合泊松模型的推广。作为应用程序，我们考虑涉及零截断几何、零截断负二项式和零截断二项式批量索赔到达的模型。我们还在由此产生的风险模型下提供了一些与废墟相关的数量。最后，通过数值示例，我们可视化这些量的行为。