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Forecasting age distribution of death counts: an application to annuity pricing

Published online by Cambridge University Press:  17 September 2019

Han Lin Shang Open the ORCID record for Han Lin Shang [Opens in a new window]  and
Steven Haberman
Han Lin Shang*
Affiliation:
Research School of Finance, Actuarial Studies and Statistics, Australian National University, Acton, Canberra, ACT 2601, Australia
Steven Haberman
Affiliation:
Cass Business School, City, University of London
*
*Correspondence to: Han L. Shang, Research School of Finance, Actuarial Studies and Statistics, Australian National University, Level 4, Building 26C, Kingsley Street, Acton, Canberra, ACT 2601, Australia. Tel: +61(2) 612 50535. Fax: +61(2) 612 50087. E-mail: hanlin.shang@anu.edu.au
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Abstract

We consider a compositional data analysis approach to forecasting the age distribution of death counts. Using the age-specific period life-table death counts in Australia obtained from the Human Mortality Database, the compositional data analysis approach produces more accurate 1- to 20-step-ahead point and interval forecasts than Lee–Carter method, Hyndman–Ullah method and two naïve random walk methods. The improved forecast accuracy of period life-table death counts is of great interest to demographers for estimating survival probabilities and life expectancy, and to actuaries for determining temporary annuity prices for various ages and maturities. Although we focus on temporary annuity prices, we consider long-term contracts that make the annuity almost lifetime, in particular when the age at entry is sufficiently high.

Keywords

Compositional data analysislife-table death countslog-ratio transformationprincipal component analysissingle-premium temporary annuity

Information

Type
Paper
Information
Annals of Actuarial Science , Volume 14 , Issue 1 , March 2020 , pp. 150 - 169
Copyright
© Institute and Faculty of Actuaries 2019 

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