We extend a recently proposed stochastic loss reserving model for liabilities from incurred but not reported (IBNR) micro-level claims. We propose viewing the number of claims from an event as a measure of catastrophic severity. This view covers catastrophes with arbitrarily many classes of magnitude. Our Markovian model allows the time between disasters to depend on the previous event’s level of severity. Simultaneously, we let the discount rate vary in the same manner. First, we find the moments of IBNR liabilities in our model. Then, we permit a later time horizon for IBNR claims when considered jointly with incurred and reported claims.

我们扩展了最近提出的随机损失准备金模型，用于已发生但未报告 (IBNR) 微观层面索赔的负债。我们建议将事件的索赔数量视为灾难严重程度的衡量标准。这种观点涵盖了任意数量级的灾难。我们的马尔可夫模型允​​许灾难之间的时间取决于先前事件的严重程度。同时，我们让贴现率以同样的方式变化。首先，我们在模型中找到了 IBNR 负债的矩。然后，当与已发生和报告的索赔一起考虑时，我们允许 IBNR 索赔的较晚时间范围。