Stochastic portfolio specific mortality and the quantification of mortality basis risk. (English) Zbl 1231.91226

Summary: In the last decade a vast literature on stochastic mortality models has been developed. However, these models are often not directly applicable to insurance portfolios because: (a) For insurers and pension funds it is more relevant to model mortality rates measured in insured amounts instead of measured in the number of policies. (b) Often there is not enough insurance portfolio specific mortality data available to fit such stochastic mortality models reliably. Therefore, in this paper a stochastic model is proposed for portfolio specific mortality experience. Combining this stochastic process with a stochastic country population mortality process leads to stochastic portfolio specific mortality rates, measured in insured amounts. The proposed stochastic process is applied to two insurance portfolios, and the impact on the value at risk for longevity risk is quantified. Furthermore, the model can be used to quantify the basis risk that remains when hedging portfolio specific mortality risk with instruments of which the payoff depends on population mortality rates.


91B30 Risk theory, insurance (MSC2010)
91B70 Stochastic models in economics
91G10 Portfolio theory
Full Text: DOI


[1] Brouhns, N.; Denuit, M.; Vermunt, J.K., A Poisson log-bilinear regression approach to the construction of projected life tables, Insurance: mathematics and economics, 31, 373-393, (2002) · Zbl 1074.62524
[2] Cairns, A.J.G.; Blake, D.; Dowd, K., A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration, Journal of risk and insurance, 73, 687-718, (2006)
[3] CEIOPS,, 2007. QIS 4 Technical Specifications
[4] Continuous Mortality Investigation (1962): Continuous investigation into the mortality of pensioners under life office pension schemes. Available at: http://www.actuaries.org.uk/knowledge/cmi
[5] Continuous Mortality Investigation (2004): Working paper 9. Available at: http://www.actuaries.org.uk/knowledge/cmi
[6] Continuous Mortality Investigation (2008): Working paper 31. Available at: http://www.actuaries.org.uk/knowledge/cmi
[7] Coughlan, G., Epstein, D., Ong, A., Sinha, A., Balevich, I., Hevia-Portocarrero, J., Gingrich, E., Khalaf-Allah, M., Joseph, P., 2007. Lifemetrics Technical Document. Available at: http://www.jpmorgan.com/pages/jpmorgan/investbk/solutions/lifemetrics
[8] Currie, I.D.; Durban, M.; Eilers, P.H.C., Smoothing and forecasting mortality rates, Statistical modelling, 4, 279-298, (2004) · Zbl 1061.62171
[9] Currie, I.D., 2006. Smoothing and forecasting mortality rates with P-splines, Talk given at the Institute of Actuaries. June. Available at: http:www.ma.hw.ac.uk/ iain/research/talks.html
[10] Dahl, M.; Møller, T., Valuation and hedging of life insurance liabilities with systematic mortality risk, Insurance: mathematics and economics, 39, 193-217, (2006) · Zbl 1201.91089
[11] Jarner, S.F., Kryger, E.M., 2009. Modelling Adult Mortality in Small Populations: The Saint Model, discussion paper, available at: http://www.pensions-institute.org/papers.html · Zbl 1239.91128
[12] Jolliffe, I.T., Principal component analysis, (2002), Springer-Verlag New York, Inc · Zbl 1011.62064
[13] Lee, R.D.; Carter, L.R., Modelling and forecasting U.S. mortality, Journal of the American statistical association, 87, 659-675, (1992) · Zbl 1351.62186
[14] Loeys, J., Panigirtzoglou, N., Ribeiro, R.M., 2007. Longevity: A market in the making. Available at: http://www.jpmorgan.com/pages/jpmorgan/investbk/solutions/lifemetrics
[15] Namboodiri, K.; Suchindran, C.M., Life table techniques and their applications, (1987), Academic Press, Inc
[16] Nelson, C.R.; Siegel, A.F., Parsimonious modeling of yield curve, Journal of business, 60, 473-489, (1987)
[17] Renshaw, A.E.; Haberman, S., A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insurance: mathematics and economics, 38, 556-570, (2006) · Zbl 1168.91418
[18] Sweeting, P., Pricing basis risk in survivor swaps, Life & pensions, September, 40-44, (2007)
[19] Van Broekhoven, H, Market value of liabilities mortality risk: A practical model, North American actuarial journal, 6, 95-106, (2002) · Zbl 1084.62555
[20] Verbeek, M., Modern econometrics, (2008), John Wiley & Sons, Ltd
[21] van Verzekeraars, Verbond, 2008, Generatietafels Pensioenen (in dutch)
[22] Zellner, A, Estimators of seemingly unrelated regressions: some exact finite sample results, Journal of the American statistical association, 58, 977-992, (1963) · Zbl 0129.11203
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.