×

Multidimensional Lee-Carter model with switching mortality processes. (English) Zbl 1235.91091

Summary: This paper proposes a multidimensional Lee-Carter model, in which the time dependent components are ruled by switching regime processes. The main feature of this model is its ability to replicate the changes of regimes observed in the mortality evolution. Changes of measure, preserving the dynamics of the mortality process under a pricing measure, are also studied. After a review of the calibration method, a 2D, 2-regimes model is fitted to the male and female French population, for the period 1946–2007. Our analysis reveals that one regime corresponds to longevity conditions observed during the decade following the second world war, while the second regime is related to longevity improvements observed during the last 30 years. To conclude, we analyze, in a numerical application, the influence of changes of measure affecting transition probabilities, on prices of life and death insurances.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bauer, D.; Bergmann, D.; Kiesel, R., On the risk-neutral valuation of life insurance contracts with numerical methods in view, ASTIN bulletin, 40, 65-95, (2010), 2 · Zbl 1230.91066
[2] Bauer, D.; Boerger, M.; Russ, J., On the pricing of longevity-linked securities, Insurance: mathematics and economics, 46, 139-149, (2010), (special issue Longevity Four) · Zbl 1231.91142
[3] Biffis, E., Blake, D., 2009. Mortality-linked securities and derivatives. Discussion Paper of the Pension Institute, PI-0901.
[4] Biffis, E.; Denuit, M.; Devolder, P., Stochastic mortality under measure changes, Scandinavian actuarial journal, 2010, 284-311, (2010) · Zbl 1226.91022
[5] Blake, D., De Waegenaere, A., McMinn, R., Nijman, T., 2009. Longevity risk and capital markets: the 2008-2009 update. Discussion Paper of the Pension Institute, Reference PI-0907.
[6] Brémaud, P., Point processes and queues-martingales dynamics, (1981), Springer Verlag
[7] Buffington, J.; Elliott, R.J., American options with regime switching, International journal of theoretical and applied finance, 5, 497-514, (2002) · Zbl 1107.91325
[8] Cairns, A.J.C., Modelling and management of mortality risk: a review, Scandinavian actuarial journal, 2-3, 79-113, (2008) · Zbl 1224.91048
[9] Cairns, A.J.G.; Blake, D.; Dowd, K., Pricing death: frameworks for the valuation and securitization of mortality risk, ASTIN bulletin, 36, 1, 79-120, (2006) · Zbl 1162.91403
[10] Gardiner, C.W., Handbook of stochastic methods, (1983), Springer Verlag · Zbl 0862.60050
[11] Hamilton, J.D., A new approach to the economic analysis of non stationary time series and the business cycle, Econometrica, 57, 2, 357-384, (1989) · Zbl 0685.62092
[12] Kusuoka, S., A remark on default risk models, (), 69-82 · Zbl 0939.60023
[13] Lee, R.D., The lee – carter method for forecasting mortality, with various extensions and applications, North American actuarial journal, 4, 80-93, (2000) · Zbl 1083.62535
[14] Lee, R.D.; Carter, L., Modelling and forecasting the time series of US mortality, Journal of the American statistical association, 87, 659-671, (1992)
[15] McDonald, A.S.; Cairns, A.J.C.; Gwilt, P.L.; Miller, K.A., An international comparison of recent trends in mortality, British actuarial journal, 4, 3-141, (1998)
[16] Milidonis, A.; Lin, Y.; Cox, S.H., Mortality regimes and pricing, North American actuarial journal, 15, 2, 266-289, (2011) · Zbl 1228.91043
[17] Pitacco, E., Survival models in a dynamic context: a survey, Insurance: mathematics and economics, 35, 279-298, (2004) · Zbl 1079.91050
[18] Protter, P., Stochastic integration and differential equations, (2004), Springer-Verlag · Zbl 1041.60005
[19] Renshaw, A.E.; Haberman, S., Lee – carter mortality forecasting with age-specific enhancement, Insurance: mathematics and economics, 33, 255-272, (2003) · Zbl 1103.91371
[20] Sweeting, P., 2009. A trend-change extension of the Cairns-Blake-Dowd model. Working Paper of the Pension Institute, Cass Business School.
[21] Wong-Fupuy, C.; Haberman, Projecting mortality trends: recent developments in the UK and US, North American actuarial journal, 8, 56-83, (2004) · Zbl 1085.62517
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.