Construction of laws of experience in the presence of competing events: Application to the estimation of incidence laws of a dependency contract.

Summary This paper proposes to illustrate the implementation of non-parametric estimation methods, introduced in the framework of Markovian multi-state models with censoring, to construct laws of experience applicable in the presence of several concurrent events. This situation arises in practice in long term care insurance when it is necessary to distinguish the incidence laws by pathology. Therefore, rather than applying techniques usually used by practitioners and consisting in observing marginally each cause of entry into dependence, the approach described allows to estimate globally all the entry laws by cause and to correctly apprehend the interdependence between each of them. This work provides a comparison of the results obtained by these two approaches at the level of the provision to be made in order to justify a marginal approach, which is simpler to implement in practice.