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Multiplicative Hazard Models for Studying the Evolution of Mortality

Published online by Cambridge University Press:  10 May 2011

M. Guillen ,
J. P. Nielsen  and
A. M. Perez-Marin
M. Guillen
Affiliation:
Department of Econometrics, University of Barcelona, Diagonal 690, E-08034 Barcelona, Spain., Email: [email protected]
J. P. Nielsen
Affiliation:
Royal&SunAlliance Codan, Gammel Kongevej 60, 1790, Copenhagen V, Denmark., Email: [email protected]
A. M. Perez-Marin
Affiliation:
Department of Econometrics, University of Barcelona, Diagonal 690, E-08034 Barcelona, Spain., Email: [email protected]
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Abstract

Almost all over the world, decreasing mortality rates and increasing life expectancy have led to greater interest in estimating and predicting mortality. Here we describe some of the pitfalls which can result from the use of the standardised mortality ratio (SMR) while evaluating the development of mortality over time, in particular when SMRs are applied to insurance portfolios varying dramatically over time. Although an excellent comparative study of a single-figure index for a number of countries was recently done by Macdonald et al. (1998), we advocate care when attempting to extend this type of method to insurance data. Here we promote the use of genuine multiplicative modelling such as in Felipe et al. (2001), who compared the mortality rates in Denmark and Spain. The starting point for our study was the two-dimensional mortality estimator of Nielsen & Linton (1995), which considers mortality as a function of chronological time and age. From the principle of marginal integration (see Nielsen & Linton, 1995, and Linton et al., 2003), estimators of the multiplicative model can be obtained from this two-dimensional estimator. An application of the method is provided for mortality data of the United States of America, England & Wales, France, Italy, Japan and Russia.

Keywords

LongevityStandardised Mortality RatioMortality Experience
Type
Papers
Information
Annals of Actuarial Science , Volume 1 , Issue 1 , March 2006 , pp. 165 - 177
Copyright
Copyright © Institute and Faculty of Actuaries 2006

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