A Stochastic Model for Mortality Rate on Italian Data

A new stochastic model for mortality rate is proposed and analyzed on Italian mortality data. The model is based on a stochastic differential equation derived from a generalization of the Milevesky and Promislow model (Milevesky, M.A., Promislow, S.D.: Insur. Math. Econ. 29, 299-318 (2001)). We discuss and present a methodology, based on the discretisation approach by Wymer (Wymer, C.R.: Econometrica 40(3), 565-577 (1972)) to evaluate the parameters of our model. The comparison with the Milevesky and Promislow model shows the relevance of our proposal along an horizon, which includes periods of time with a different volatility of mortality rates. The estimate of the parameters turns out to be stable over time with the exception of the mean reverting parameter, which shows, for a person of a fixed age, an increase over time.