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 costs 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 costs. 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, as discussed in Gneiting and A. E. Raftery (2007)

翻译：我们提出了一种基于条件Aalen–Johansen估计量的个体索赔准备金模型，该估计量由Bladt和Furrer（2023b）发展而来。在我们的方法中，我们构建了一个多状态问题，其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期，我们利用条件Aalen–Johansen方法估计个体索赔成本的累积分布函数，将其视为转移至吸收状态的转移概率。我们的方法重新诠释了多状态模型的概念，并为个体索赔成本的完整曲线建模提供了一种策略。为阐明该方法，我们将模型应用于模拟数据集和真实数据集。由于能够访问完整数据集，我们通过比较预测的最终总成本与实际金额，以及根据Gneiting和A. E. Raftery（2007）提出的连续排序概率得分进行评估，来支持该方法的应用。