(Contribution of a SCOR expert in an external publication) The pricing of today's long-term care insurance products relies on simple models where dependency is considered as a single homogeneous state. Because of aging population and rapid evolution in the field of medicine, it becomes paramount to get a clearer picture of the underlying risk. We believe it may only be achieved by taking into account several levels of dependency. A semi-Markov process is a multi-state process whose transition probabilities not only depend on the current state but also on the time spent in this state. This process has proven more flexible than the simple Markov process, and is core to numerous publications in the field of epidemiology. However its use in relation with long-term care insurance has remained mostly theoretical, mainly because of the lack of data available to insurers. The present article aims at introducing the construction process of a semi-Markov model with 4 levels of dependency. This work is based on data from the French long-term care public aid: the "Allocation Personnalisée d'Autonomie" (APA). Firstly, we introduce the parameters used to model transitions between states. We then proceed to the calibration of those parameters, using a likelihood maximization method, while taking into account the peculiarities of the APA data set. Finally, we apply this model to the pricing of a fictive long-term care insurance product, using a Monte Carlo method.
Bulletin français d'actuariat n°29 / vol. 15 / Janvier 2015 - Juin 2015