A multivariate evolutionary credibility model for mortality improvement rates. (English) Zbl 1369.91097

Summary: The present paper proposes an evolutionary credibility model that describes the joint dynamics of mortality through time in several populations. Instead of modeling the mortality rate levels, the time series of population-specific mortality rate changes, or mortality improvement rates are considered and expressed in terms of correlated time factors, up to an error term. Dynamic random effects ensure the necessary smoothing across time, as well as the learning effect. They also serve to stabilize successive mortality projection outputs, avoiding dramatic changes from one year to the next. Statistical inference is based on maximum likelihood, properly recognizing the random, hidden nature of underlying time factors. Empirical illustrations demonstrate the practical interest of the approach proposed in the present paper.


91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
91D20 Mathematical geography and demography


Human Mortality
Full Text: DOI


[1] Börger, M., Aleksic, M.-C., 2014. Coherent projections of age, period, and cohort dependent mortality improvements. In: Living to 100 Symposium. Orlando, Fla. January, Vol. 8, p. 2014.
[2] Brockwell, P. J.; Davis, R. A., Time series: theory and methods, (2006), Springer · Zbl 0673.62085
[3] Bühlmann, H.; Gisler, A., A course in credibility theory and its applications, (2005), Springer · Zbl 1108.91001
[4] Carter, L. R.; Lee, R. D., Modeling and forecasting us sex differentials in mortality, Int. J. Forecast., 8, 3, 393-411, (1992)
[5] Coelho, E.; Nunes, L. C., Forecasting mortality in the event of a structural change, J. Roy. Statist. Soc. Ser. A, 174, 3, 713-736, (2011)
[6] Czado, C.; Delwarde, A.; Denuit, M., Bayesian Poisson log-bilinear mortality projections, Insurance Math. Econom., 36, 3, 260-284, (2005) · Zbl 1110.62142
[7] Debón, A.; Montes, F.; Martínez-Ruiz, F., Statistical methods to compare mortality for a group with non-divergent populations: an application to Spanish regions, Eur. Actuar. J., 1, 2, 291-308, (2011)
[8] Delwarde, A.; Denuit, M.; Guillen, M.; Vidiella, A., Application of the Poisson log-bilinear projection model to the g5 mortality experience, Belg. Actuar. Bull., 6, 1, 54-68, (2006) · Zbl 1356.91056
[9] Girosi, F.; King, G., Demographic forecasting, (2008), Princeton University Press
[10] Hamilton, J. D., Time series analysis, vol. 2, (1994), Princeton University Press Princeton
[11] Human-Mortality-Database, 2015. University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Available at www.mortality.org or www.humanmortality.de (data downloaded on May 2nd, 2015).
[12] Hunt, A.; Blake, D., A general procedure for constructing mortality models, N. Am. Actuar. J., 18, 1, 116-138, (2014) · Zbl 1412.91045
[13] Hunt, A.; Blake, D., Modelling longevity bonds: analysing the swiss re kortis bond, Insurance Math. Econom., 63, 12-29, (2015) · Zbl 1348.91150
[14] Kogure, A.; Kitsukawa, K.; Kurachi, Y., A Bayesian comparison of models for changing mortalities toward evaluating longevity risk in Japan, Asia-Pac. J. Risk. Insur., 3, 2, 1-22, (2009)
[15] Kogure, A.; Kurachi, Y., A Bayesian approach to pricing longevity risk based on risk-neutral predictive distributions, Insurance Math. Econom., 46, 1, 162-172, (2010) · Zbl 1231.91438
[16] Lee, R. D.; Carter, L. R., Modeling and forecasting us mortality, J. Amer. Statist. Assoc., 87, 419, 659-671, (1992) · Zbl 1351.62186
[17] Li, J., A Poisson common factor model for projecting mortality and life expectancy jointly for females and males, Popul. Stud., 67, 1, 111-126, (2013)
[18] Li, J., An application of MCMC simulation in mortality projection for populations with limited data, Demogr. Res., 30, 1, 1-48, (2014)
[19] Li, N.; Lee, R., Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method, Demography, 42, 3, 575-594, (2005)
[20] Mitchell, D.; Brockett, P.; Mendoza-Arriaga, R.; Muthuraman, K., Modeling and forecasting mortality rates, Insurance Math. Econom., 52, 2, 275-285, (2013) · Zbl 1284.91259
[21] Pedroza, C., A Bayesian forecasting model: predicting us male mortality, Biostatistics, 7, 4, 530-550, (2006) · Zbl 1170.62397
[22] Russolillo, M.; Giordano, G.; Haberman, S., Extending the Lee-Carter model: a three-way decomposition, Scand. Actuar. J., 2011, 2, 96-117, (2011) · Zbl 1277.62260
[23] Sundt, B., Recursive credibility estimation, Scand. Actuar. J., 1981, 1, 3-21, (1981) · Zbl 0463.62093
[24] Yang, S. S.; Wang, C.-W., Pricing and securitization of multi-country longevity risk with mortality dependence, Insurance Math. Econom., 52, 2, 157-169, (2013) · Zbl 1284.91556
[25] Yashin, A. I.; Iachine, I. A.; Begun, A. Z.; Vaupel, J. W., Hidden frailty: myths and reality, (2001), Department of Statistics and Demography Odense University
[26] Zhou, R.; Li, J. S.-H.; Tan, K. S., Pricing standardized mortality securitizations: A two-population model with transitory jump effects, J. Risk Insur., 80, 3, 733-774, (2013)
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.