A Bayesian Joint Model for Population and Portfolio-Specific Mortality

31 Pages Posted: 20 Nov 2015 Last revised: 17 May 2017

See all articles by Frank van Berkum

Frank van Berkum

University of Amsterdam - Department of Quantitative Economics (KE)

Katrien Antonio

KU Leuven; University of Amsterdam

Michel Vellekoop

University of Amsterdam - Faculty of Economics and Business (FEB)

Date Written: December 2016

Abstract

Insurers and pension funds must value liabilities using mortality rates that are appropriate for their portfolio. Current practice is to multiply available projections of population mortality with portfolio-specific factors, which are often determined using Generalised Linear Models. Alternatively, one of the well-known stochastic mortality models can directly be applied to portfolio data to construct portfolio-specific projections without the use of population data. However, this requires a sufficiently large historical dataset for the portfolio, which is often not available.

We overcome this problem by introducing a model to estimate portfolio-specific mortality simultaneously with population mortality. We use a Bayesian framework, which automatically generates the appropriate weighting of the limited statistical information for a given portfolio and the more extensive information that is available for the whole population. It also allows us to incorporate parameter uncertainty when projecting portfolio-specific mortality rates.

We apply our method to a dataset of assured lives in England & Wales. We find that uncertainty in portfolio-specific factors can be significant, and that confidence intervals for portfolio-specific mortality projections are slightly wider than those resulting from frequentist projections.

Keywords: Bayesian analysis, portfolio-specific mortality, mortality experience, random effects, smoothing prior, simultaneous modelling

Suggested Citation

Berkum, Frank van and Antonio, Katrien and Vellekoop, Michel, A Bayesian Joint Model for Population and Portfolio-Specific Mortality (December 2016). Netspar Discussion Paper No. 11/2015-034. Available at SSRN: https://ssrn.com/abstract=2692605 or http://dx.doi.org/10.2139/ssrn.2692605

Frank van Berkum (Contact Author)

University of Amsterdam - Department of Quantitative Economics (KE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

Katrien Antonio

KU Leuven ( email )

Leuven, Vlaams-Brabant

HOME PAGE: http://www.econ.kuleuven.be/katrien.antonio

University of Amsterdam ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

Michel Vellekoop

University of Amsterdam - Faculty of Economics and Business (FEB) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

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