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A BAYESIAN JOINT MODEL FOR POPULATION AND PORTFOLIO-SPECIFIC MORTALITY

Published online by Cambridge University Press:  18 July 2017

Frank van Berkum ,
Katrien Antonio  and
Michel Vellekoop
Frank van Berkum*
Affiliation:
Faculty of Economics and Business, University of Amsterdam, Amsterdam, The Netherlands
Katrien Antonio
Affiliation:
Faculty of Economics and Business, University of Amsterdam, Amsterdam, The Netherlands, Faculty of Economics and Business, KU Leuven, Belgium
Michel Vellekoop
Affiliation:
Faculty of Economics and Business, University of Amsterdam, Amsterdam, The Netherlands
*
E-Mail: f.vanberkum@uva.nl
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Abstract

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Insurance companies and pension funds must value liabilities using mortality rates that are appropriate for their portfolio. These can only be estimated in a reliable way from a sufficiently large historical dataset for such portfolios, which is often not available. We overcome this problem by introducing a model to estimate portfolio-specific mortality simultaneously with population mortality. By using a Bayesian framework, we automatically generate the appropriate weighting for the limited statistical information in a given portfolio and the more extensive information that is available for the whole population. This allows us to separate parameter uncertainty from uncertainty due to the randomness in individual deaths for a given realization of mortality rates. When we apply our method to a dataset of assured lives in England and Wales, we find that different prior specifications for the portfolio-specific factors lead to significantly different posterior distributions for hazard rates. However, in short-term predictive distributions for future numbers of deaths, individual mortality risk turns out to be more important than parameter uncertainty in the portfolio-specific factors, both for large and for small portfolios.

Keywords

Bayesian analysisportfolio-specific mortalitymortality projectionvon Mises–Fisher priorsmoothing prior
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 3 , September 2017 , pp. 681 - 713
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
Copyright © Astin Bulletin 2017

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