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SMOOTHING POISSON COMMON FACTOR MODEL FOR PROJECTING MORTALITY JOINTLY FOR BOTH SEXES

Published online by Cambridge University Press:  09 January 2018

David Pitt ,
Jackie Li  and
Tian Kang Lim
David Pitt
Affiliation:
Department of Applied Finance and Actuarial Studies, Macquarie University, NSW 2109, Australia E-Mail: [email protected]
Jackie Li*
Affiliation:
Department of Applied Finance and Actuarial Studies, Macquarie University, NSW 2109, Australia
Tian Kang Lim
Affiliation:
Department of Applied Finance and Actuarial Studies, Macquarie University, NSW 2109, Australia E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

We consider a modification to the Poisson common factor model and utilise a generalised linear model (GLM) framework that incorporates a smoothing process and a set of linear constraints. We extend the standard GLM model structure to adopt Lagrange methods and P-splines such that smoothing and constraints are applied simultaneously as the parameters are estimated. Our results on Australian, Canadian and Norwegian data show that this modification results in an improvement in mortality projection in terms of producing more accurate forecasts in the out-of-sample testing. At the same time, projected male-to-female ratio of death rates at each age converges to a constant and the residuals of the models are sufficiently random, indicating that the use of smoothing does not adversely affect the fit of the model. Further, the irregular patterns in the estimates of the age-specific parameters are moderated as a result of smoothing and this model can be used to produce more regular projected life tables for pricing purposes.

Keywords

Generalised linear modelsPoisson common factor modelsmoothingjoint modelling of both sexes
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 2 , May 2018 , pp. 509 - 541
Copyright
Copyright © Astin Bulletin 2018 

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