Abstract
The mortality dynamics experienced in the latest decades, especially at adult and old ages, has motivated the introduction of major innovations in the modeling of mortality for actuarial applications; such innovations concern, in particular, the representation of the uncertainty relating to aggregate mortality.
In this paper, we first provide a description of the traditional mortality model which is deterministic but also allows quite easily for a representation of the uncertainty relating to individual mortality. Then, we discuss a stochastic approach to the modeling of the uncertainty relating to aggregate mortality. Due to the importance of mortality evolution in respect of post-retirement liabilities, we refer to a portfolio of immediate life annuities (or pension annuities). We assume that a (projected) life table which provides a best-estimate assessment of annuitants’ future mortality is available. We show that the life table, from which a deterministic description of future mortality can be obtained, can be used as the basic input of appropriate stochastic models. In particular, we consider a Bayesian-inference setting for updating the parameters of the stochastic model according to the experienced mortality.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Biffis, E.: Affine processes for dynamic mortality and actuarial valuations. Insur. Math. Econ. 37(3), 443–468 (2005)
Biffis, E., Millossovich, P.: A bidimensional approach to mortality risk. Decis. Econ. Finance 29, 71–94 (2006)
Bühlmann, H.: Mathematical Methods in Risk Theory. Springer, New York (1970)
Cairns, A.J.G.: A multifactor generalisation of the Olivier–Smith model for stochastic mortality. In: Proceedings of the 1st IAA-Life Colloquium, Stockholm (2007)
Cairns, A.J.G., Blake, D., Dowd, K.: Pricing death: Frameworks for the valuation and securitization of mortality risk. ASTIN Bull. 36(1), 79–120 (2006)
Carlin, B.P., Louis, T.A.: Bayes and Empirical Bayes Methods for Data Analysis. Chapman & Hall / CRC, Boca Raton (2000)
CMI: An interim basis for adjusting the “92” series mortality projections for cohort effects. Working Paper 1, The Faculty of Actuaries and Institute of Actuaries (2002)
CMI: Stochastic projection methodologies: Further progress and P-spline model features, example results and implications. Working Paper 20, The Faculty of Actuaries and Institute of Actuaries (2006)
Dahl, M.: Stochastic mortality in life insurance. Market reserves and mortality-linked insurance contracts. Insur. Math. Econ. 35(1), 113–136 (2004)
Dahl, M., Møller, T.: Valuation and hedging of life insurance liabilities with systematic mortality risk. Insur. Math. Econ. 39(2), 193–217 (2006)
Haberman, S., Olivieri, A.: Risk classification / Life. In: Melnick, E., Everitt, B. (eds.) The Encyclopedia of Quantitative Risk Assessment and Analysis, pp. 1535–1540. Wiley, Chichester (2008)
Hardy, M.R., Panjer, H.H.: A credibility approach to mortality risk. ASTIN Bull. 28(2), 269–283 (1998)
Lee, R., Carter, L.R.: Modelling and forecasting U.S. mortality. J. Am. Stat. Assoc. 87(14), 659–675 (1992)
Li, J.S.H., Hardy, M.R., Tan, K.S.: Uncertainty in mortality forecasting: An extension to the classic Lee-Carter approach. ASTIN Bull. 39(1), 137–164 (2009)
Marocco, P., Pitacco, E.: Longevity risk and life annuity reinsurance. In: Transactions of the 26th International Congress of Actuaries, Birmingham, vol. 6, pp. 453–479 (1998)
Olivier, P., Jeffrey, T.: Stochastic mortality models. Presentation to the Society of Actuaries in Ireland (2004)
Olivieri, A.: Uncertainty in mortality projections: An actuarial perspective. Insur. Math. Econ. 29(2), 231–245 (2001)
Olivieri, A.: Heterogeneity in survival models. Applications to pensions and life annuities. Belg. Actuar. Bull. 6, 23–39 (2006)
Olivieri, A.: Stochastic mortality: Experience-based modeling and application issues consistent with Solvency 2. Eur. Actuar. J. 1(Suppl. 1), S101–S125 (2011)
Olivieri, A., Pitacco, E.: Inference about mortality improvements in life annuity portfolios. In: Transactions of the 27th International Congress of Actuaries, Cancun (Mexico) (2002)
Olivieri, A., Pitacco, E.: Solvency requirements for pension annuities. J. Pension Econ. Finance 2, 127–157 (2003)
Olivieri, A., Pitacco, E.: Stochastic mortality: The impact on target capital. ASTIN Bull. 39(2), 541–563 (2009)
Panjer, H., Willmot, G.: Insurance Risk Models. The Society of Actuaries, Schaumberg (1992)
Pitacco, E.: From Halley to “frailty”: A review of survival models for actuarial calculations. G. Ist. Ital. Attuari 67(1–2), 17–47 (2004)
Pitacco, E., Denuit, M., Haberman, S., Olivieri, A.: Modelling Longevity Dynamics for Pensions and Annuity Business. Oxford University Press, Oxford (2009)
Robert, C.D., Casella, G.: Monte Carlo Statistical Methods. Springer, Berlin (2004)
Smith, A.D.: Stochastic mortality modelling. Talk at the Workshop on the Interface between Quantitative Finance and Insurance, International Centre for Mathematical Science, Edinburgh (2005)
Sweeting, P.J.: Making the most of experience data—An augmented Beta-Binomial approach. Discussion Paper PI-1012, The Pension Institute, Cass Business School, City University, London (2010)
Tuljapurkar, S., Boe, C.: Mortality change and forecasting: How much and how little do we know. N. Am. Actuar. J. 2(4), 13–47 (1998)
Vaupel, J.W., Manton, K.G., Stallard, E.: The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16(3), 439–454 (1979)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Olivieri, A., Pitacco, E. Life tables in actuarial models: from the deterministic setting to a Bayesian approach. AStA Adv Stat Anal 96, 127–153 (2012). https://doi.org/10.1007/s10182-011-0177-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10182-011-0177-y