Multistate models for long-term care insurance and related indexing problems (Q2711712)

Multistate modelling is a modern stochastic approach which provides the actuary with a powerful tool for designing and implementing life and health insurance products and for interpreting conventional actuarial assumptions. Owing to this approach, a ``new'' life insurance mathematics has been developed and applications to several health insurance products have been studied. In particular, multistate modelling provides a flexible tool for expressing the actuarial structure of several long-term care (LTC) products such as fixed-amount annuities (possibly depending on the disability level). A time-continuous, multistate approach is adopted for expressing the actuarial structure of LTC covers. In this framework, the problem of linking LTC benefits to some index is analysed. A systematic approach for analysing several types of indexing in life insurance policies and pension schemes has been proposed by \textit{T. Pentikäinen} [in: Trans. 18th Int. Congr. of Actuaries, Munich, 2, 847-859 (1968)]. From the financial point of view, the Pentikäinen approach is a conventional one, in the sense that fixed, non-stochastic inflation and interest rates are considered. A simple and flexible model allows to take into account ex-post adjustment, based on several indexes (such as inflation rates, yields from investments, etc.). In this article, the same approach is adopted, as far as the financial structure is concerned, to analyse the possibility of indexing LTC benefits. However, the indexing problem is embedded in a general multistate framework.