# Periodic or generational actuarial tables: which one to choose?

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## Abstract

The increase in life expectancy over the past several decades has been impressive and represents a key challenge for institutions that provide life insurance products. Indeed, when a new actuarial table is released with updated survival and death rates, such institutions need to update the amount of mathematical reserve that they need to set aside to guarantee the future payments of their annuities. As mortality forecasting techniques are currently well developed, it is relatively easy to forecast mortality over several decades and to directly use these forecast rates in the determination of the mathematical reserve needed to guarantee annuity payments. Future mortality evolution is then directly incorporated into the liabilities valuation of an institution, and it is thus commonly believed that such liabilities should not require much updating when a new actuarial table is released. In this paper, we demonstrate that contrary to this common belief, institutions that use generational tables (namely, tables including future mortality evolution) will most likely need to make more important adjustments (positive or negative) to their liabilities than will institutions using periodic (static) tables whenever a new table is released. By using three very different models to project mortality, we demonstrate that our findings are inherent in the required long horizons of the forecasts needed in the generational approach, with the uncertainty surrounding the forecast values increasing with the horizon. Therefore, generational tables may introduce more instability in a pension institution’s accounts than periodic tables.

## Keywords

Mortality rates Periodic actuarial tables Generational actuarial tables Life expectancy Mathematical reserve Mortality forecasts## Notes

### Acknowledgements

We are grateful to Geert Coene and Bas Werker for useful discussions about the various models used in this work. We are grateful to the Human Mortality Database and the Office Fédéral de la Statistique for having provided us with the tables used in this work.

## References

- 1.Alho J (2000) Discussion of Lee. N Am Actuar J 4:91–93CrossRefGoogle Scholar
- 2.Antonio K, Devriendt S, de Boer W, de Vries R, De Waegenaere A, Kan H-K, Kromme E, Ouburg W, Schulteis T, Slagter E, Vellekoop M, van der Winden M, van Lersel C (2016) Producing the Dutch and Belgian mortality projections: A stochastic multi-population standard. Technical Report N. 554572, Department of Accounting, Finance and InsuranceGoogle Scholar
- 3.Brouhns N, Denuit M, Vermunt J (2002) A Poisson log-bilinear regression approach to the construction of projected life tables. Insur Math Econ 31:373–393CrossRefzbMATHGoogle Scholar
- 4.Cairns A, Blake D, Dowd K (2006a) Pricing death: frameworks for the valuation and securitization of mortality risk. ASTIN Bull 36:79–120MathSciNetCrossRefzbMATHGoogle Scholar
- 5.Cairns A, Blake D, Dowd K (2006b) A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. J Risk Insur 73(4):687–718CrossRefGoogle Scholar
- 6.Cairns A, Blake D, Dowd K, Coughlan G, Epstein D, Ong A, Balevich I (2009) A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. N Am Actuar J 13(1):1–35MathSciNetCrossRefGoogle Scholar
- 7.Cairns A, Blake D, Dowd K, Coughlan G, Epstein,D, Khalaf-Allah M (2011) Mortality density forecasts: an analysis of six stochastic mortality models. Insur Math Econ 48:355–367MathSciNetCrossRefzbMATHGoogle Scholar
- 8.CMI (2016) CMI mortality projections model consultation-technical paper. In: Technical report, Continuous Mortality Investigation. WP 91Google Scholar
- 9.De Grey ADNJ (2006) Extrapolaholics anonymous: why demographers’ rejections of a huge rise in cohort life expectancy in this century are overconfident. Ann N Y Acad Sci 1067:83–93CrossRefGoogle Scholar
- 10.Delwarde A, Denuit M, Eilers P (2007) Smoothing the Lee-Carter and Poisson log-bilinear models for mortality forecasting. Stat Model 7:29–48MathSciNetCrossRefGoogle Scholar
- 11.Dowd K, Cairns A, Blake D, Coughlan G, Epstein D, Khalaf-Allah M (2010) Backtesting stochastic mortality models. N Am Actuar J 14(3):281–298MathSciNetCrossRefzbMATHGoogle Scholar
- 12.Gaille S (2012) Forecasting mortality: when academia meets practice. Eur Actuar J 2(1):49–76MathSciNetCrossRefzbMATHGoogle Scholar
- 13.Gerber H (1995) Life insurance mathematics. Springer, BerlinCrossRefzbMATHGoogle Scholar
- 14.Haberman S, Renshaw A (2009) On age-period-cohort parametric mortality rate projections. Insur Math Econ 45:255–270MathSciNetCrossRefzbMATHGoogle Scholar
- 15.Haberman S, Renshaw A (2011) A comparative study of parametric mortality projection models. Insur Math Econ 48:35–55MathSciNetCrossRefGoogle Scholar
- 16.S Haberman, Renshaw A (2012) Parametric mortality improvement rate modelling and projecting. Insur Math Econ 50:309–333MathSciNetCrossRefzbMATHGoogle Scholar
- 17.Hayflick L (2004) “Anti-Aging” Is an oxymoron. J Gerontol Biol Sci 59A(6):573–578CrossRefGoogle Scholar
- 18.Henderson R (1924) A new method of graduation. Trans Actuar Soc Am 25:29–53Google Scholar
- 19.Hodrick R, Prescott E (1997) Postwar US business cycles: an empirical investigation. J Money Credit Bank 29(1):1–16CrossRefGoogle Scholar
- 20.Kannistö V (1992) Development of the oldest-old mortality, 1950–1980: evidence from 28 developed countries. Odense University Press, OdenseGoogle Scholar
- 21.Lee R D, Carter L R (1992) Modeling and forecasting US-mortality. J Am Stat Assoc 87(419):659–671zbMATHGoogle Scholar
- 22.Li N, Lee R (2005) Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method. Demography 42:575–594CrossRefGoogle Scholar
- 23.Menthonnex J (2006) Tables de mortalité longitudinales pour la Suisse. In: Technical report, SCRISGoogle Scholar
- 24.Menthonnex J (2009) La mortalité par génération en Suisse: Evolution 1900–2150 et tables par génération 1900–2030. In: Technical report, Statistique Vaud-SCRISGoogle Scholar
- 25.Menthonnex J (2015) Estimation des durées de vie par génération: Evolution 1900–2150 et tables de mortalité par génération 1900–2030 pour la Suisse. In: Technical report, Office fédéral de la statistique OFSGoogle Scholar
- 26.Olshansky SJ, Hayflick L, Carnes BA (2002) Position statement on human aging. J Gerontol Biol Sci 57A(8):B292–B297CrossRefGoogle Scholar
- 27.Pitacco E, Denuit M, Haberman S, Olivieri A (2009) Modeling longevity dynamics for pensions and annuity business. Oxford University Press, LondonzbMATHGoogle Scholar
- 28.Whittaker E (1923) On a new method of graduation. Proc Edinb Math Soc 41:63–73Google Scholar