In the classical Lee-Carter model, the mortality indices that are assumed to be a random walk model with drift are normally distributed. However, for the long-term mortality data, the error terms of the Lee-Carter model and the mortality indices have tails thicker than those of a normal distribution and appear to be skewed. This study therefore adopts five nonGaussian distributions-Student's t-distribution and its skew extension (i.e., generalised hyperbolic skew Student's t-distribution), one finite-activity Le´vy model (jump diffusion distribution), and two infinite-activity or pure jump models (variance gamma and normal inverse Gaussian)-to model the error terms of the Lee-Carter model. With mortality data from six countries over the period 1900-2007, both in-sample model selection criteria (e.g., Bayesian information criterion, Kolmogorov-Smirnov test, Anderson-Darling test, Crame´r-von-Mises test) and out-of-sample projection errors indicate a preference for modelling the Lee-Carter model with non-Gaussian innovations.

This article provides an iterative fitting algorithm to generate maximum likelihood estimates under the Cox regression model and employs non-Gaussian distributions-the jump diffusion (JD), variance gamma (VG), and normal inverse Gaussian (NIG) distributions-to model the error terms of the Renshaw and Haberman (2006) (RH) model. In terms of mean absolute percentage error, the RH model with non-Gaussian innovations provides better mortality projections, using 1900-2009 mortality data from England and Wales, France, and Italy. Finally, the lower hedge costs of longevity swaps according to the RH model with non-Gaussian innovations are not only based on the lower swap curves implied by the best prediction model, but also in terms of the fatter tails of the unexpected losses it generates.Chou-Wen Wang is a Professor in the