Consider a by-claim risk model with a constant force of interest, where each main claim may induce a by-claim after a random time. We propose a time-claim-dependent framework, that incorporates dependence between not only the waiting time and the claim but also the main claim and the corresponding by-claim. Based on this framework, we derive some asymptotic estimates for the finite-time ruin probabilities in the case of subexponential claims. We also provide examples and verify the assumptions on dependence. Numerical studies are conducted to examine the performance of these asymptotic formulas.

中文翻译：

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具有相关次指数索赔的时间相关索赔模型的渐近

考虑具有恒定利益力的副索赔风险模型，其中每个主要索赔可能会在随机时间后引发副索赔。我们提出了一个与时间声明相关的框架，该框架不仅包含等待时间和声明之间的依赖关系，还包含主声明和相应的副声明之间的依赖关系。基于这个框架，我们得出了次指数索赔情况下有限时间破产概率的一些渐近估计。我们还提供了示例并验证了关于依赖性的假设。进行数值研究来检验这些渐近公式的性能。