A health insurance pricing model based on prevalence rates: Application to critical illness insurance

The Italian health insurance market is currently undersized. The paucity of assured data and the discon- tinuous statistical surveys carried out by the National Institute of Statistics (ISTAT) represent one of the main obstacles to the insurance market development. The paper sets forth a parametric model to estimate technical basis for health insurance policies when data are limited and only aggregated information on mortality and morbidity is available. The probabilistic framework is based on a multiple state continu- ous and time inhomogeneous Markov model. We provide an estimate of transition intensities from the healthy state to the sickness state when only prevalence rates of sickness are available, according to an extension and modification of the methodology proposed in Olivieri (1996) for Long Term Care insur- ance. We assume that mortality intensity of both healthy and sick lives is modelled by two independent Gompertz–Makeham models.