Stochastic Models for Disability: Approximations and Applications to Sickness and Personal Accident Insurance

Abstract

In actuarial practice, the main calculations for insurance covers in the health care area, personal accident and sickness insurance in particular, are commonly based on simplified methods, whose probabilistic assumptions are often not enough clear. In this paper, starting from a rather general structure for the disability process, we show that reasonable approximations lead to the multistate model. Thus, we first show that, since the features of the multistate model allow for several disability degrees, a rigorous modelling for personal accident insurance can be obtained; in this context, risk factors (and hence rating factors) can be represented by an appropriate choice of the transition intensities. Secondly, as the multistate model provides a sound framework for interpreting practical calculation methods used in the health insurance area, we revise some pricing formulae for personal accident and sickness insurance used in practice, so to highlight the main underlying probabilistic assumptions.