We propose an individual claims reserving model based on the conditional Aalen-Johansen estimator, as developed in Bladt and Furrer (2023b). In our approach, we formulate a multi-state problem, where the underlying variable is the individual claim size, rather than time. The states in this model represent development periods, and we estimate the cumulative density function of individual claim sizes using the conditional Aalen-Johansen method as transition probabilities to an absorbing state. Our methodology reinterprets the concept of multi-state models and offers a strategy for modeling the complete curve of individual claim sizes. To illustrate our approach, we apply our model to both simulated and real datasets. Having access to the entire dataset enables us to support the use of our approach by comparing the predicted total final cost with the actual amount, as well as evaluating it in terms of the continuously ranked probability score.

翻译：本文提出了一种基于条件Aalen-Johansen估计量的个体索赔准备金评估模型，该方法由Bladt与Furrer（2023b）的研究发展而来。在我们的方法中，我们构建了一个多状态问题，其中基础变量是个体索赔金额而非时间。该模型中的状态代表发展周期，我们使用条件Aalen-Johansen方法作为向吸收状态的转移概率，来估计个体索赔金额的累积分布函数。我们的方法重新诠释了多状态模型的概念，并为个体索赔金额完整曲线的建模提供了一种策略。为说明该方法，我们将模型应用于模拟数据集和真实数据集。通过获取完整数据集，我们能够通过比较预测总最终成本与实际金额来验证方法的有效性，并基于连续排序概率评分进行评估。