Mortality Modeling a State-Space approach with Non-Gaussian Error Component

Abstract

The improvements of mortality in recent years have started a worrying trend for many actuaries. To tackle this issue researchers have developed. stochastic mortality models to better capture future changes in mortality, however with recent advancements in the econometric literature, we are able to focus on parameter estimation in mortality modeling. This paper aims to apply recent econometric techniques used in State$-$Space models to mortality modeling. Firstly, a State$-$Space representation to the Lee$-$Carter model is formed, one common approach is to assume Gaussian error terms in the measurement equation as this will simplify the estimation procedure to a linear$-$Gaussian case and the Kalman Filter can be used directly. However, the Kalman Filter breaks down in the case where a more realistic error component is used such as the Poisson error. In this paper we approximate a Poisson error structure via a Gaussian$-$Mixture model and apply Kalman Filtering in a Bayesian method, for a frequentist method a Quasi$-$Maximum Likelihood approach is used. We then test the bayesian$-$frequentist forecast coverage and its implications to actuarial pricing.

Melvern Leung

Manager - Risk Model Validation

My research interests include distributed robotics, mobile computing and programmable matter.