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An Augmented Variable Dirichlet Process mixture model for the analysis of dependent lifetimes

Published online by Cambridge University Press:  02 December 2024

Francesco Ungolo Open the ORCID record for Francesco Ungolo [Opens in a new window]  and
Patrick J. Laub
Francesco Ungolo*
Affiliation:
School of Risk and Actuarial Studies University of New South Wales Kensington, NSW 2052, Australia ARC Centre of Excellence in Population Ageing Research, University of New South Wales Kensington, NSW 2052, Australia
Patrick J. Laub
Affiliation:
School of Risk and Actuarial Studies University of New South Wales Kensington, NSW 2052, Australia
*
Corresponding author: Francesco Ungolo; Email: [email protected]
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Abstract

The analysis of insurance and annuity products issued on multiple lives requires the use of statistical models which account for lifetime dependence. This paper presents a Dirichlet process mixture-based approach that allows to model dependent lifetimes within a group, such as married couples, accounting for individual as well as group-specific covariates. The model is analyzed in a fully Bayesian setting and illustrated to jointly model the lifetime of male–female couples in a portfolio of joint and last survivor annuities of a Canadian life insurer. The inferential approach allows to account for right censoring and left truncation, which are common features of data in survival analysis. The model shows improved in-sample and out-of-sample performance compared to traditional approaches assuming independent lifetimes and offers additional insights into the determinants of the dependence between lifetimes and their impact on joint and last survivor annuity prices.

Keywords

Dependent lifetimessurvival analysisDirichlet processBayesian analysislife insuranceMCMCmixture models
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 55 , Issue 1 , January 2025 , pp. 50 - 75
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The International Actuarial Association

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