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Multi-population mortality modelling and forecasting: a hierarchical credibility regression approach. (English) Zbl 1479.91307

Summary: This paper proposes a multi-level hierarchical credibility regression approach to model multi-population mortality data. Future mortality rates are derived using extrapolation techniques, while the forecasting performances between the proposed model, the original Lee-Carter model and two Lee-Carter extensions for multiple populations are compared for both genders of three northern European countries with small populations (Ireland, Norway, Finland). Empirical illustrations show that the proposed method produces more accurate forecasts than the Lee-Carter model and its multi-population extensions.

MSC:

91G05 Actuarial mathematics
91D20 Mathematical geography and demography
62P05 Applications of statistics to actuarial sciences and financial mathematics
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[1] Antonio, K.; Bardoutsos, A.; Ouburg, W., Bayesian Poisson log-bilinear models for mortality projections with multiple populations, Eur Actuar J, 5, 2, 245-281 (2015) · Zbl 1329.91111
[2] Apicella, G.; Dacorogna, M.; Di Lorenzo, E.; Sibillo, M., Improving the forecast of longevity by combining models, N Am Actuar J, 23, 2, 298-319 (2019) · Zbl 1410.91253
[3] Bauwelinckx, T.; Goovaerts, MJ, On a multilevel hierarchical credibility algorithm, Insur Math Econ, 9, 221-228 (1990) · Zbl 0714.62100
[4] Bozikas, A.; Pitselis, G., Credible regression approaches to forecast mortality for populations with limited data, Risks, 7, 1, 27 (2019)
[5] Bozikas, A.; Pitselis, G., Incorporating crossed classification credibility into the Lee-Carter model for multi-population mortality data, Insur Math Econ, 93, 353-368 (2020) · Zbl 1448.91257
[6] Bühlmann, H., Experience rating and credibility, ASTIN Bull, 4, 3, 199-207 (1967)
[7] Bühlmann, H.; Straub, E., Glaubwürdigkeit für schadensätze, Bull Swiss Assoc Actuaries, 70, 111-133 (1970) · Zbl 0197.46502
[8] Bühlmann, H.; Gisler, A., A course in credibility theory and its applications (2005), New York: Springer, New York · Zbl 1108.91001
[9] Cairns, AJ; Blake, D.; Dowd, K., A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration, J Risk Insur, 73, 4, 687-718 (2006)
[10] Cairns, AJ; Blake, D.; Dowd, K.; Coughlan, GD; Khalaf-Allah, M., Bayesian stochastic mortality modeling for two populations, ASTIN Bull, 41, 1, 29-59 (2011) · Zbl 1228.91032
[11] Carter, LR; Lee, RD, Modeling and forecasting US sex differentials in mortality, Int J Forecast, 8, 3, 393-411 (1992)
[12] Chen, H.; MacMinn, R.; Sun, T., Multi-population mortality models: a factor copula approach, Insur Math Econ, 63, 135-146 (2015) · Zbl 1348.91131
[13] Chen, RY; Millossovich, P., Sex-specific mortality forecasting for UK countries: a coherent approach, Eur Actuar J, 8, 1, 69-95 (2018) · Zbl 1416.91163
[14] D’Amato, V.; Haberman, S.; Piscopo, G.; Russolillo, M., Modelling dependent data for longevity projections, Insur Math Econ, 51, 3, 694-701 (2012) · Zbl 1285.91054
[15] D’Amato, V.; Haberman, S.; Piscopo, G.; Russolillo, M.; Trapani, L., Detecting common longevity trends by a multiple population approach, N Am Actuar J, 18, 1, 139-149 (2014) · Zbl 1412.91041
[16] De Vylder, FE, Geometrical credibility, Scand Actuar J, 1976, 3, 121-149 (1976) · Zbl 0345.62082
[17] De Vylder FE (1996) Advanced risk theory: a self-contained introduction. Ed. de l’Univ. de Bruxelles
[18] Diao, L.; Weng, C., Regression tree credibility model, N Am Actuar J, 23, 2, 169-196 (2019) · Zbl 1410.91264
[19] Dowd, K.; Cairns, AJ; Blake, D.; Coughlan, GD; Khalaf-Allah, M., A gravity model of mortality rates for two related populations, N Am Actuar J, 15, 2, 334-356 (2011) · Zbl 1228.91032
[20] Frees, EW; Shi, P.; Valdez, EA, Actuarial applications of a hierarchical insurance claims model, ASTIN Bull, 39, 1, 165-197 (2009)
[21] Frees, EW; Valdez, EA, Hierarchical insurance claims modeling, J Am Stat Assoc, 103, 484, 1457-1469 (2008) · Zbl 1286.62087
[22] Frees, EW; Young, VR; Luo, Y., A longitudinal data analysis interpretation of credibility models, Insur Math Econ, 24, 3, 229-247 (1999) · Zbl 0945.62112
[23] Gong, Y.; Li, Z.; Milazzo, M.; Moore, K.; Provencher, M., Credibility methods for individual life insurance, Risks, 6, 4, 144 (2018)
[24] Goovaerts, MJ; Kaas, R.; Van Heerwaarden, AE; Bauwelinckx, T., Effective actuarial methods (1990), Amsterdam: North-Holland, Amsterdam
[25] Hachemeister, C.; Kahn, P., Credibility for regression models with application to trend (reprint), Credibility: theory and applications, 307-348 (1975), New York: Academic Press, Inc., New York
[26] Hahn, LJ; Christiansen, MC, Mortality projections for non-converging groups of populations, Eur Actuar J, 9, 483-518 (2019) · Zbl 1433.91132
[27] Hardy, MR; Panjer, HH, A credibility approach to mortality risk, ASTIN Bull, 28, 2, 269-283 (1998) · Zbl 1162.91415
[28] Hatzopoulos, P.; Haberman, S., A parameterized approach to modeling and forecasting mortality, Insur Math Econ, 44, 1, 103-123 (2009) · Zbl 1156.91394
[29] Hatzopoulos, P.; Haberman, S., A dynamic parameterization modeling for the age-period-cohort mortality, Insur Math Econ, 49, 155-174 (2011) · Zbl 1218.91082
[30] Human Mortality Database (2018) University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). https://www.mortality.org. Accessed 23 Oct 2018
[31] Hyndman, RJ; Ullah, MS, Robust forecasting of mortality and fertility rates: A functional data approach, Comput Stat Data Anal, 51, 10, 4942-4956 (2007) · Zbl 1162.62434
[32] Jewell, WS, The use of collateral data in credibility theory: a hierarchical model, Giornale dell’Istituto Italiano degli Attuari, 38, 1-16 (1975) · Zbl 0392.62086
[33] Kleinow, T., A common age effect model for the mortality of multiple populations, Insur Math Econ, 63, 147-152 (2015) · Zbl 1348.91233
[34] Klugman, SA; Panjer, HH; Willmot, GE, Loss models: from data to decisions (2012), New York: Wiley, New York · Zbl 1272.62002
[35] Lee, RD; Carter, LR, Modeling and forecasting U.S. mortality, J Am Stat Assoc, 87, 419, 659-671 (1992) · Zbl 1351.62186
[36] Li, JSH; Hardy, MR, Measuring basis risk in longevity hedges, N Am Actuar J, 15, 2, 177-200 (2011) · Zbl 1228.91042
[37] Li, JSH; Zhou, R.; Hardy, M., A step-by-step guide to building two-population stochastic mortality models, Insur Math Econ, 63, 121-134 (2015) · Zbl 1348.91164
[38] 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)
[39] Lin, T.; Tsai, CCL, A simple linear regression approach to modeling and forecasting mortality rates, J Forecast, 34, May, 543-559 (2015) · Zbl 1365.62478
[40] Norberg, R., Empirical Bayes credibility, Scand Actuar J, 1980, 4, 177-194 (1980) · Zbl 0447.62107
[41] Norberg, R., Hierarchical credibility: analysis of a random effect linear model with nested classification, Scand Actuar J, 3-4, 204-222 (1986) · Zbl 0649.62099
[42] Ohlsson E (2005) Simplified estimation of structure parameters in hierarchical credibility. In: The 36th ASTIN Colloquium, Zürich (2005). http://www.actuaries.org/ASTIN/Colloquia/Zurich/Ohlsson.pdf. Accessed 28 Sep 2020
[43] Ohlsson, E., Combining generalized linear models and credibility models in practice, Scand Actuar J, 2008, 4, 301-314 (2008) · Zbl 1224.91080
[44] Plat, R., On stochastic mortality modeling, Insur Math Econ, 45, 3, 393-404 (2009) · Zbl 1231.91227
[45] R Core Team (2018) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/. Accessed 20 Dec 2018
[46] Renshaw, AE; Haberman, S., A cohort-based extension to the Lee-Carter model for mortality reduction factors, Insur Math Econ, 38, 3, 556-570 (2006) · Zbl 1168.91418
[47] Salhi, Y.; Thérond, PE, Age-specific adjustment of graduated mortality, ASTIN Bull, 48, 2, 543-569 (2018) · Zbl 1390.62220
[48] Salhi, Y.; Thérond, PE; Tomas, J., A credibility approach of the Makeham mortality law, Eur Actuar J, 6, 1, 61-96 (2016) · Zbl 1415.91163
[49] Schinzinger, E.; Denuit, MM; Christiansen, MC, A multivariate evolutionary credibility model for mortality improvement rates, Insur Math Econ, 69, 70-81 (2016) · Zbl 1369.91097
[50] Sundt, B., A hierarchical credibility regression model, Scand Actuar J, 1979, 2-3, 107-114 (1979) · Zbl 0418.62087
[51] Sundt, B., A multi-level hierarchical credibility regression model, Scand Actuar J, 1980, 1, 25-32 (1980) · Zbl 0432.62074
[52] Taylor, GC, Credibility analysis of a general hierarchical model, Scand Actuar J, 1979, 1, 1-12 (1979) · Zbl 0399.62105
[53] Tsai, CCL; Lin, T., A Bühlmann credibility approach to modeling mortality rates, N Am Actuar J, 21, 2, 204-227 (2017) · Zbl 1414.91237
[54] Tsai, CCL; Lin, T., Incorporating the Bühlmann credibility into mortality models to improve forecasting performances, Scand Actuar J, 5, 419-440 (2017) · Zbl 1401.91198
[55] Tsai, CCL; Wu, AD, Incorporating hierarchical credibility theory into modelling of multi-country mortality rates, Insur Math Econ, 91, 37-54 (2020) · Zbl 1435.91160
[56] Tsai, CCL; Wu, AD, Bühlmann credibility-based approaches to modeling mortality rates for multiple populations, N Am Actuar J, 24, 2, 290-315 (2020) · Zbl 1455.91229
[57] Tsai, CCL; Zhang, Y., A multi-dimensional Bühlmann credibility approach to modeling multi-population mortality rates, Scand Actuar J, 5, 406-431 (2019) · Zbl 1411.91317
[58] Wilson, C., On the scale of global demographic convergence 1950-2000, Populat Dev Rev, 27, 155-171 (2001)
[59] Zehnwirth, B., Conditional linear Bayes rules for hierarchical models, Scand Actuar J, 1982, 3-4, 143-154 (1982) · Zbl 0497.62031
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