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Exchangeable mortality projection. (English) Zbl 1482.91189

The increasing of the life expectancy has serious financial implications. Changes in mortality need to be accurately predicted because the government policies, funds allocation for government services, pricing life annuities and reserve calculations have to be based on reliable mortality forecasting. The most popular model for mortality forecasting is the classical Lee-Carter model in which it is supposed that mortality is a function of age and year of death.
Authors of the paper analyse various modification of the Lee-Carter model and derive the new multi-population Lee-Carter type model in which the exchangeability is allowed between parameters of a group of populations. The proposed forecasting model is being tested for several groups of countries.

MSC:

91G05 Actuarial mathematics
91D20 Mathematical geography and demography
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[1] Achana, FA; Cooper, NJ; Bujkiewicz, S.; Hubbard, SJ; Kendrick, D.; Jones, DR; Sutton, AJ, Network meta-analysis of multiple outcome measures accounting for borrowing of information across outcomes, BMC Med Res Methodol, 14, 1, 1 (2014)
[2] Ahcan, A.; Medved, D.; Olivieri, A.; Pitacco, E., Forecasting mortality for small populations by mixing mortality data, Insur Math Econ, 54, 12-27 (2014)
[3] Alexander, M.; Zagheni, E.; Barbieri, M., A flexible Bayesian model for estimating subnational mortality, Demography, 54, 6, 2025-2041 (2017)
[4] Alkema, L.; Raftery, AE; Gerland, P.; Clark, SJ; Pelletier, F.; Buettner, T.; Heilig, GK, Probabilistic projections of the total fertility rate for all countries, Demography, 48, 3, 815-839 (2011)
[5] 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
[6] Biatat VD, Currie ID (2010) Joint models for classification and comparison of mortality in different countries. In: Proceedings of 25rd international workshop on statistical modelling, Glasgow, pp 89-94
[7] Booth, H.; Maindonald, J.; Smith, L., Applying Lee-Carter under conditions of variable mortality decline, Popul Stud, 56, 3, 325-336 (2002)
[8] Box, GEP; Tiao, GC, Bayesian estimation of means for the random effect model, J Am Stat Assoc, 63, 174-181 (1968) · Zbl 0157.47902
[9] Brouhns, N.; Denuit, M.; Vermunt, JK, Measuring the longevity risk in mortality projections, Bull Swiss Assoc Actuar, 2, 105-130 (2002) · Zbl 1187.62158
[10] Brouhns, N.; Denuit, M.; Vermunt, JK, A Poisson log-bilinear regression approach to the construction of projected lifetables, Insur Math Econ, 31, 3, 373-393 (2002) · Zbl 1074.62524
[11] Butt Z, Haberman S (2009) ilc: a collection of R functions for fitting a class of Lee-Carter mortality models using iterative fitting algorithms. http://openaccess.city.ac.uk/2321/
[12] Cairns, AJG; Blake, D.; Dowd, K.; Coughlan, GD; Khalaf-Allah, M., Bayesian stochastic mortality modelling for two populations, Astin Bull, 41, 1, 29-59 (2011) · Zbl 1228.91032
[13] Carter, LR; Lee, RD, Modeling and forecasting US sex differentials in mortality, Int J Forecast, 8, 3, 393-411 (1992)
[14] Carter LR, Prskawetz A (2001) Examining structural shifts in mortality using the Lee-Carter method. Methoden und Ziele 39
[15] Coelho E, Nunes L (2013) Cohort effects and structural changes in the mortality trend. In: Technical report. Working paper. http://www.unece.org/fileadmin/DAM/stats/documents/ece/ces/ge.11/2013/WP5.1.pdf.
[16] Czado, C.; Delwarde, A.; Denuit, M., Bayesian Poisson log-bilinear mortality projections, Insur Math Econ, 36, 3, 260-284 (2005) · Zbl 1110.62142
[17] Danesi, IL; Haberman, S.; Millossovich, P., Forecasting mortality in subpopulations using Lee-Carter type models: a comparison, Insur Math Econ, 62, 151-161 (2015) · Zbl 1318.91109
[18] 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)
[19] De Finetti, B., La prévision: ses lois logiques, ses sources subjectives, Annales de l’institut Henri Poincaré, 7, 1-68 (1937) · Zbl 0017.07602
[20] Delwarde, A.; Denuit, M.; Guillén, M.; Vidiella-i Anguera, A., Application of the Poisson log-bilinear projection model to the G5 mortality experience, Belgian Actuar Bull, 6, 1, 54-68 (2006) · Zbl 1356.91056
[21] Denuit M, Goderniaux A (2005) Closing and projecting lifetables using log-linear models. Bull Swiss Assoc Actuari, p 29 · Zbl 1333.62251
[22] Fuse, M.; Yamasue, E.; Reck, BK; Graedel, TE, Regional development or resource preservation? A perspective from Japanese appliance exports, Ecol Econ, 70, 4, 788-797 (2011)
[23] Geman, S.; Geman, D., Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans Pattern Anal Mach Intelli, 6, 721-741 (1984) · Zbl 0573.62030
[24] Gilks, WR; Wild, P., Adaptive rejection sampling for Gibbs sampling, J R Stat Soc, 41, 2, 337-348 (1992) · Zbl 0825.62407
[25] Gill, J., Bayesian methods: a social and behavioral sciences approach (2007), Cambridge: CRC press, Cambridge · Zbl 1130.62114
[26] Gottardo, R.; Li, W.; Johnson, WE; Liu, XS, A flexible and powerful Bayesian hierarchical model for ChIP-chip experiments, Biometrics, 64, 2, 468-478 (2008) · Zbl 1137.62394
[27] Greco F, Scalone F (2013) A space-time extension of the Lee-Carter model in a hierarchical Bayesian framework: modelling and forecasting provincial mortality in Italy. https://pdfs.semanticscholar.org/62c2/d02a22557042def54fa1ce1467808835a05a.pdf
[28] Halstead, BJ; Wylie, GD; Coates, PS; Valcarcel, P.; Casazza, ML, Bayesian shared frailty models for regional inference about wildlife survival, Anim Conserv, 15, 2, 117-124 (2012)
[29] Hong, H.; Chu, H.; Zhang, J.; Carlin, BP, A Bayesian missing data framework for generalized multiple outcome mixed treatment comparisons, Res Synth Methods, 7, 1, 6-22 (2016)
[30] Human Mortality Database. University of California Berkeley (USA) and Max Planck Institute for Demographic Research (Germany). www.mortality.org. Accessed 20 June 2016
[31] Janssen, F.; Kunst, A., The choice among past trends as a basis for the prediction of future trends in old-age mortality, Popul Stud, 61, 3, 315-326 (2007)
[32] Kasim, RM; Raudenbush, SW, Application of Gibbs sampling to nested variance components models with heterogeneous within-group variance, J Educ Behav Stat, 23, 2, 93-116 (1998)
[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] Kogure, A.; Kurachi, Y., A Bayesian approach to pricing longevity risk based on risk-neutral predictive distributions, Insur Math Econ, 46, 1, 162-172 (2010) · Zbl 1231.91438
[35] Kogure A, Kitsukawa K, Kurachi Y (2009) A Bayesian comparison of models for changing mortalities toward evaluating longevity risk in Japan. Asia Pac J Risk Insur 3(2)
[36] Lee, RD; Carter, LR, Modeling and forecasting US mortality, J Am Stat Assoc, 87, 419, 659-671 (1992) · Zbl 1351.62186
[37] Lee, R.; Miller, T., Evaluating the performance of the Lee-Carter method for forecasting mortality, Demography, 38, 4, 537-549 (2001)
[38] Leonard, T., Bayesian methods for binomial data, Biometrika, 59, 3, 581-589 (1972) · Zbl 0263.62025
[39] 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)
[40] Li, J., An application of MCMC simulation in mortality projection for populations with limited data, Demogr Res, 30, 1-48 (2014)
[41] Li, JS-H; Hardy, MR, Measuring basis risk in longevity hedges, N Am Actuar J, 15, 2, 177-200 (2011) · Zbl 1228.91042
[42] 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)
[43] Lindley, DV, Bayesian statistics: a review (1972), New Delhi: SIAM, New Delhi · Zbl 0246.62009
[44] Lindley, DV; Novick, MR, The role of exchangeability in inference, Ann Stat, 9, 45-58 (1981) · Zbl 0473.62005
[45] Li, N.; Lee, R.; Tuljapurkar, S., Using the Lee-Carter method to forecast mortality for populations with limited data*, Int Stat Rev, 72, 1, 19-36 (2004) · Zbl 1330.62349
[46] Li, H.; De Waegenaere, A.; Melenberg, B., The choice of sample size for mortality forecasting: a Bayesian learning approach, Insur Math Econ, 63, 153-168 (2015) · Zbl 1348.91162
[47] Maiti, T., Hierarchical Bayes estimation of mortality rates for disease mapping, J Stat Plan Inference, 69, 2, 339-348 (1998) · Zbl 0935.62124
[48] Owen, RK; Tincello, DG; Keith, RA, Network meta-analysis: development of a three-level hierarchical modeling approach incorporating dose-related constraints, Value Health, 18, 1, 116-126 (2015)
[49] Papadatou, E.; Pradel, R.; Schaub, M.; Dolch, D.; Geiger, H.; Ibañez, C.; Kerth, G.; Popa-Lisseanu, A.; Schorcht, W.; Teubner, J., Comparing survival among species with imperfect detection using multilevel analysis of mark-recapture data: a case study on bats, Ecography, 35, 2, 153-161 (2012)
[50] Pedroza, C., A Bayesian forecasting model: predicting US male mortality, Biostatistics, 7, 4, 530-550 (2006) · Zbl 1170.62397
[51] Renshaw, AE; Haberman, S., Lee-Carter mortality forecasting with age-specific enhancement, Insur Math Econ, 33, 2, 255-272 (2003) · Zbl 1103.91371
[52] 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
[53] Shair, S.; Purcal, S.; Parr, N., Evaluating extensions to coherent mortality forecasting models, Risks, 5, 1, 16 (2017)
[54] Shang HL, Hyndman RJ, Booth H, et al. (2010) A comparison of ten principal component methods for forecasting mortality rates
[55] Smith, AFM, A general Bayesian linear model, J R Stat Soc Ser B Methodol, 35, 67-75 (1973) · Zbl 0256.62055
[56] Son, YS; Oh, M., Bayesian analysis of the two-parameter gamma distribution, Commun Stat Simul Comput, 35, 285-293 (2006) · Zbl 1093.62036
[57] Tsionas, EG, Exact inference in four-parameter generalized gamma distributions, Commun Stat Theory Methods, 30, 747-756 (2001) · Zbl 1009.62526
[58] Tuljapurkar, S.; Li, N.; Boe, C., A universal pattern of mortality decline in the G7 countries, Nature, 405, 6788, 789-792 (2000)
[59] Villegas, AM; Haberman, S., On the modeling and forecasting of socioeconomic mortality differentials: an application to deprivation and mortality in England, N Am Actuar J, 18, 1, 168-193 (2014) · Zbl 1412.91057
[60] Villegas, AM; Haberman, S.; Kaishev, VK; Millossovich, P., A comparative study of two-population models for the assessment of basis risk in longevity hedges, ASTIN Bull J IAA, 47, 3, 631-679 (2017) · Zbl 1390.91215
[61] Warren, FC; Abrams, KR; Sutton, AJ, Hierarchical network meta-analysis models to address sparsity of events and differing treatment classifications with regard to adverse outcomes, Stat Med, 33, 14, 2449-2466 (2014)
[62] Wilmoth J, Valkonen T (2001) A parametric representation of mortality differentials over age and time. In: Fifth seminar of the EAPS working group on differentials in health, morbidity and mortality in Europe, Pontignano, Italy
[63] Wiśniowski, A.; Smith, PWF; Bijak, J.; Raymer, J.; Forster, JJ, Bayesian population forecasting: extending the Lee-Carter method, Demography, 52, 3, 1035-1059 (2015)
[64] Yang, B.; Li, J.; Balasooriya, U., Cohort extensions of the Poisson common factor model for modelling both genders jointly, Scand Actuar J, 2016, 2, 93-112 (2016) · Zbl 1401.91203
[65] Yang, SS; Wang, C-W, Pricing and securitization of multi-country longevity risk with mortality dependence, Insur Math Econ, 52, 2, 157-169 (2013) · Zbl 1284.91556
[66] Yang S, Yue JC, Yeh Y-Y (2011) Coherent mortality modeling for a group of populations. In: Living to 100 symposium
[67] Zhou, R.; Wang, Y.; Kaufhold, K.; Li, JS-H; Tan, K. S., Modeling period effects in multi-population mortality models: applications to Solvency II, N Am Actuar J, 18, 1, 150-167 (2014) · Zbl 1412.91060
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