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：我们提出一种基于条件Aalen-Johansen估计量的个体索赔准备金模型，该估计量由Bladt和Furrer（2023b）提出。在该方法中，我们构建了一个多状态问题，其中核心变量为个体索赔金额而非时间。模型中的各状态代表发展期，我们通过条件Aalen-Johansen方法估计个体索赔金额的累积分布函数，将其视为到达吸收状态的转移概率。该研究重新诠释了多状态模型的概念，并提供了对个体索赔金额完整曲线建模的策略。为验证该方法的有效性，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的支持，我们能够将预测总最终成本与实际金额进行对比，并基于连续排序概率评分对其进行评估。