Geiger Daniel J, Adekpedjou Akim
Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409 USA.
Methodol Comput Appl Probab. 2022;24(2):815-829. doi: 10.1007/s11009-022-09950-5. Epub 2022 Jun 22.
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一种针对已发生但未报告（IBNR）微观层面索赔负债的随机损失准备金模型。我们建议将某一事件的索赔数量视为灾难严重程度的一种度量。这种观点涵盖了具有任意多等级规模的灾难。我们的马尔可夫模型允许灾难之间的时间间隔取决于前一事件的严重程度水平。同时，我们让贴现率以相同方式变化。首先，我们在我们的模型中求出IBNR负债的矩。然后，当与已发生和已报告索赔一起考虑时，我们允许IBNR索赔有一个更晚的时间范围。
