Stochastic Mortality Modelling : Some Extensions Based on Lévy CARMA Models

Force of mortality is defined using an exponential function of Legendre polynomials, as in Renshaw et al. (1996), plus an extra term which captures mortality shocks. For the extra term Ballotta Haberman (2006) and Ahmadi et al. (2015) consider an Ornstein-Uhlenbeck while we suggest using Lévy Continuous Autoregressive Moving Average (CARMA) models. The proposed model encompasses as special cases the existing approaches. We present some extensions in the theory of Lévy CARMA models that enter in the construction of the model estimation procedure. Males life tables for USA, Taiwan and Japan for the time period 1998-2013 are used for the presentation of fitting and projection results