  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.
