Automatic Indexation of the Pension Age to Life Expectancy: When Policy Design Matters
Open accessAbstract
Increasing retirement ages in an automatic or scheduled way with increasing life expectancy at retirement is a popular pension policy response to continuous longevity improvements. The question addressed here is: to what extent is simply adopting this approach likely to fulfill the overall goals of policy? To shed some light on the answer, we examine the policies of four countries that have recently introduced automatic indexation of pension ages to life expectancy–The Netherlands, Denmark, Portugal and Slovakia. To this end, we forecast an alternative period and cohort life expectancy measures using a Bayesian Model Ensemble of heterogeneous stochastic mortality models comprised of parametric models, principal component methods, and smoothing approaches. The approach involves both the selection of the model confidence set and the determination of optimal weights. Model-averaged Bayesian credible prediction intervals are derived accounting for various stochastic process, model, and parameter risks. The results show that: (i) retirement ages are forecasted to increase substantially in the coming decades, particularly if a constant period in retirement is targeted; (ii) retirement age policy outcomes may substantially deviate from the policy goal(s) depending on the design adopted and its implementation; and (iii) the choice of a cohort over period life expectancy measure matters. In addition, the distributional issues arising with the increasing socio-economic gap in life expectancy remain largely unaddressed.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Ensemble methods can provide superior predictive accuracy relative to single learners in several domain-specific areas.
“Empirical studies show that they can provide superior predictive accuracy relative to single learners in several domain-specific areas (Ashofteh et al. 2022; Ayuso et al. 2021; Bravo 2021; Kim and Baek 2022).”
From Modelling Motor Insurance Claim Frequency and Severity Using Gradient Boosting (2023) · cites this paper as Ayuso et al. 2021
The Introduction states that ensemble learning has improved traditional and machine-learning forecasts, supporting the possibility of better predictive accuracy. The Results discuss mortality-forecasting model weights but do not compare the ensemble’s accuracy with single models; this paper also does not establish the claim across several domain-specific areas. The supplied copy gives section labels but no page numbers. (LLM, conf=0.81)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
The Association Between Income and Life Expectancy in the United States, 2001–2014
Chetty, R., Stepner, M., Abraham, S., Lin, S., Scuderi, B., Turner, N., Bergeron, A., & Cutler, D. (2016) · JAMA · doi:10.1001/jama.2016.4226 · Cited by 2,812 · see citing works
Hansen, P. R., Lunde, A., & Nason, J. M. (2011) · Econometrica · doi:10.3982/ecta5771 · Cited by 2,153 · see citing works
Using Bayesian model averaging to calibrate forecast ensembles.
Raftery, A. E., Gneiting, T., Balabdaoui, F., & Polakowski, M. (2005) · Monthly Weather Review · doi:10.1175/mwr2906.1 · Cited by 1,915 · see citing works
Modeling and Forecasting U.S. Mortality
Lee, R. D., & Carter, L. R. (1992) · Journal of the American Statistical Association · doi:10.1080/01621459.1992.10475265 · Cited by 1,845 · see citing works
Statistical and machine learning forecasting methods: Concerns and ways forward
Makridakis, S., Spiliotis, E., & Assimakopoulos, V. (2018) · PLOS ONE · doi:10.1371/journal.pone.0194889 · Cited by 1,528 · see citing works
A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration
Cairns, A. J. G., Blake, D. P., & Dowd, K. (2006) · Journal of Risk & Insurance · doi:10.1111/j.1539-6975.2006.00195.x · Cited by 891 · see citing works
A cohort-based extension to the Lee–Carter model for mortality reduction factors
Renshaw, A. E., & Haberman, S. (2006) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2005.12.001 · Cited by 762 · see citing works
A Poisson log-bilinear regression approach to the construction of projected lifetables
Brouhns, N., Denuit, M. M., & Vermunt, J. K. (2002) · Insurance Mathematics and Economics · doi:10.1016/s0167-6687(02)00185-3 · Cited by 753 · see citing works
Robust forecasting of mortality and fertility rates: A functional data approach
Hyndman, R. J., & Ullah, M. S. (2006) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2006.07.028 · Cited by 677 · see citing works
Cairns, A. J. G., Blake, D. P., Dowd, K., Coughlan, G. D., EPSTEIN, D. A., Ong, A., & Balevich, I. (2009) · North American Actuarial Journal · doi:10.1080/10920277.2009.10597538 · Cited by 663 · see citing works
Lee–Carter mortality forecasting with age-specific enhancement
Renshaw, A. E., & Haberman, S. (2003) · Insurance Mathematics and Economics · doi:10.1016/s0167-6687(03)00138-0 · Cited by 419 · see citing works
On stochastic mortality modeling
Plat, R. (2009) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2009.08.006 · Cited by 264 · see citing works
Koissi, M.-C., Shapiro, A. F., & Högnäs, G. (2005) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2005.06.008 · Cited by 210 · see citing works
A comparative study of parametric mortality projection models
Haberman, S., & Renshaw, A. E. (2010) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2010.09.003 · Cited by 187 · see citing works
The Simple Analytics of a Pooled Annuity Fund
Piggott, J., Valdez, E. A., & Detzel, B. (2005) · Journal of Risk & Insurance · doi:10.1111/j.1539-6975.2005.00134.x · Cited by 176 · see citing works
Bootstrapping the Poisson log-bilinear model for mortality forecasting
Brouhns, N., Denuit, M. M., & Keilegom, I. V. (2005) · Scandinavian Actuarial Journal · doi:10.1080/03461230510009754 · Cited by 170 · see citing works
Zaninotto, P., Batty, G. D., Stenholm, S., Kawachi, I. I., Hyde, M., Goldberg, M., Westerlund, H., Vahtera, J., & Head, J. A. (2020) · The Journals of Gerontology Series A · doi:10.1093/gerona/glz266 · Cited by 118 · see citing works
A global view on the effects of work on health in later life
Staudinger, U. M., Finkelstein, R., Calvo, E., & Sivaramakrishnan, K. (2016) · The Gerontologist · doi:10.1093/geront/gnw032 · Cited by 118 · see citing works
Optimal retirement income tontines
Milevsky, M. A., & Salisbury, T. S. (2015) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2015.05.002 · Cited by 115 · see citing works
Shang, H. L., Booth, H., & Hyndman, R. J. (2011) · Demographic Research · doi:10.4054/demres.2011.25.5 · Cited by 113 · see citing works
How the Growing Gap in Life Expectancy May Affect Retirement Benefits and Reforms
Auerbach, A. J., Charles, K., Coile, C., Gale, W. G., Goldman, D. P., Lee, R. D., Lucas, C., Orszag, P. R., Sheiner, L., Tysinger, B., et al. (2017) · National Bureau of Economic Research · doi:10.3386/w23329 · Cited by 108 · see citing works
Optimal consumption and portfolio choice for pooled annuity funds
Stamos, M. Z. (2007) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2007.09.010 · Cited by 100 · see citing works
Nonfinancial Defined Contribution Pension Schemes in a Changing Pension World
Holzmann, R., Palmer, E., & Robalino, D. A. (2012) · World Bank, Washington, DC eBooks · doi:10.1596/978-0-8213-9478-6 · Cited by 86 · see citing works
Self-citationThe Analysis of Two-Way Functional Data Using Two-Way Regularized Singular Value Decompositions
Huang, J. Z., Shen, H., & Buja, A. (2009) · Journal of the American Statistical Association · doi:10.1198/jasa.2009.tm08024 · Cited by 86 · see citing works
Addressing Longevity Heterogeneity in Pension Scheme Design and Reform
Ayuso, M., Bravo, J. M., & Holzmann, R. (2016) · Journal of Finance & Economics · doi:10.12735/jfe.v6n1p1 · Cited by 71 · see citing works
Self-citationA COMPARATIVE STUDY OF TWO-POPULATION MODELS FOR THE ASSESSMENT OF BASIS RISK IN LONGEVITY HEDGES
Villegas, A. M., Haberman, S., Kaishev, V. K., & Millossovich, P. (2017) · Astin Bulletin · doi:10.1017/asb.2017.18 · Cited by 69 · see citing works
Robustness and convergence in the Lee–Carter model with cohort effects
Hunt, A., & Villegas, A. M. (2015) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2015.05.004 · Cited by 68 · see citing works
The Model Confidence SetPreprint
Hansen, P. R., Lunde, A., & Nason, J. M. (2004) · SSRN Electronic Journal · doi:10.2139/ssrn.522382 · Cited by 66 · see citing works
Model Confidence Sets and forecast combination
Samuels, J. D., & Sekkel, R. (2016) · International Journal of Forecasting · doi:10.1016/j.ijforecast.2016.07.004 · Cited by 65 · see citing works
Consistent dynamic affine mortality models for longevity risk applications
Blackburn, C., & Sherris, M. (2013) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2013.04.007 · Cited by 65 · see citing works
Getting life expectancy estimates right for pension policy: period versus cohort approach
Ayuso, M., Bravo, J. M., & Holzmann, R. (2020) · Journal of Pensions Economics and Finance · doi:10.1017/s1474747220000050 · Cited by 64 · see citing works
Self-citationDemand and adverse selection in a pooled annuity fund
Valdez, E. A., Piggott, J., & Wang, L. “. (2006) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2006.02.011 · Cited by 60 · see citing works
On the Structure and Classification of Mortality Models
Hunt, A., & Blake, D. P. (2020) · North American Actuarial Journal · doi:10.1080/10920277.2019.1649156 · Cited by 60 · see citing works
Bravo, J. M., & Herce, J. A. (2020) · Journal of Pensions Economics and Finance · doi:10.1017/s1474747220000189 · Cited by 58 · see citing works
Self-citationClosing and projecting life tables using log-linear models
Denuit, M. M., & Goderniaux, A. (2005) · DIAL (Catholic University of Leuven) · doi:10.5169/seals-967316 · Cited by 57 · see citing works
Addressing the life expectancy gap in pension policy
Bravo, J. M., Ayuso, M., Holzmann, R., & Palmer, E. (2021) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2021.03.025 · Cited by 56 · see citing works
Self-citationSmooth constrained mortality forecasting
Camarda, C. G. (2019) · Demographic Research · doi:10.4054/demres.2019.41.38 · Cited by 52 · see citing works
Model-averaged Wald confidence intervals
Turek, D., & Fletcher, D. (2012) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2012.03.002 · Cited by 49 · see citing works
Valuation of longevity-linked life annuities
Bravo, J. M., & de Freitas, N. E. M. (2017) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2017.09.009 · Cited by 48 · see citing works
Self-citationAyuso, M., Bravo, J. M., & Holzmann, R. (2016) · SSRN Electronic Journal · doi:10.2139/ssrn.2810471 · Cited by 46 · see citing works
Self-citationPricing Participating Longevity-Linked Life Annuities: A Bayesian Model Ensemble approach
Bravo, J. M. (2022) · European Actuarial Journal · doi:10.1007/s13385-021-00279-w · Cited by 40 · see citing works
Self-citationIntergenerational actuarial fairness when longevity increases: Amending the retirement age
Bravo, J. M., Ayuso, M., Holzmann, R., & Palmer, E. (2023) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2023.08.007 · Cited by 35 · see citing works
Self-citationModel-averaged Wald confidence intervals
TurekDaniel, & FletcherDavid (2012) · Computational Statistics & Data Analysis · Cited by 32 · see citing works
Pricing longevity derivatives via Fourier transforms
Bravo, J. M., & Nunes, J. P. V. (2020) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2020.10.008 · Cited by 30 · see citing works
Self-citationFunding for longer lives. Retirement wallet and risk-sharing annuities
Bravo, J. M. (2019) · Ekonomiaz Revista Vasca de Economía · doi:10.69810/ekz.1333 · Cited by 29 · see citing works
Self-citationRobust regularized singular value decomposition with application to mortality data
Zhang, L., Shen, H., & Huang, J. Z. (2013) · The Annals of Applied Statistics · doi:10.1214/13-aoas649 · Cited by 29 · see citing works
Detecting Common Longevity Trends by a Multiple Population Approach
D’Amato, V., Haberman, S., Piscopo, G., Russolillo, M., & Trapani, L. (2014) · North American Actuarial Journal · doi:10.1080/10920277.2013.875884 · Cited by 28 · see citing works
ROBUST REGULARIZED SINGULAR VALUE DECOMPOSITION WITH APPLICATION TO MORTALITY DATAPreprint
Zhang, L., Shen, H., & Huang, J. Z. (2013) · Cited by 25 · see citing works
Taxation of pensions in portugal: A semi-dual income tax system
Bravo, J. M. (2016) · RePEc: Research Papers in Economics · Cited by 22 · see citing works
Self-citationHolzmann, R., Palmer, E., Palacios, R., & Sacchi, S. (2019) · World Bank, Washington, DC eBooks · doi:10.1596/978-1-4648-1453-2 · Cited by 22 · see citing works
Self-citationNDC Schemes and Heterogeneity in Longevity: Proposals for RedesignPreprint
Holzmann, R., Alonso‐García, J., Hardy, H. L., & Villegas, A. M. (2017) · SSRN Electronic Journal · doi:10.2139/ssrn.3087570 · Cited by 22 · see citing works
Self-citationForecasting the Retirement Age: A Bayesian Model Ensemble Approach
Bravo, J. M., & Ayuso, M. (2021) · Advances in intelligent systems and computing · doi:10.1007/978-3-030-72657-7_12 · Cited by 21 · see citing works
Self-citationBravo, J. M., & Ayuso, M. (2020) · RISTI - Revista Ibérica de Sistemas e Tecnologias de Informação · doi:10.17013/risti.40.128-145 · Cited by 18 · see citing works
Self-citationLongevity-Linked Life Annuities: A Bayesian Model Ensemble Pricing Approach
Bravo, J. M. (2020) · Journal of the Association for Information Systems · Cited by 10 · see citing works
Self-citationAn Indexation Mechanism for Retirement Age: Analysis of the Gender Gap
Coppola, M., Russolillo, M., & Simone, R. (2019) · Risks · doi:10.3390/risks7010021 · Cited by 7 · see citing works
Holzmann, R., Ayuso, M., Alaminos, E., & Bravo, J. M. (2019) · SSRN Electronic Journal · doi:10.2139/ssrn.3468603 · Cited by 7 · see citing works
Self-citationRetirement Ages by Socio-Economic Class
Arnold, S., & Jijiie, A. (2020) · Risks · doi:10.3390/risks8040102 · Cited by 4 · see citing works
Flagged first, then by citations
Research works printed but not linked: 16
- Ayuso, Mercedes, Jorge M. Bravo, and Robert Holzmann. 2017b. Addressing longevity heterogeneity in pension scheme design. Journal of Finance and Economics 6: 1-21.
- Ayuso, Mercedes, Jorge M. Bravo, and Robert Holzmann. 2021. Getting Life Expectancy Estimates Right for Pension Policy: Period versus Cohort Approach. Journal of Pension Economics and Finance 20: 212-31.
- Bravo, Jorge M., and Jose A. Herce. 2020. Career breaks, Broken pensions? Long-run effects of early and late-career unemployment spells on pension entitlements. Journal of Pension Economics and Finance 1-27.
- Rocha, H. Adeli, G. Dzemyda, F. Moreira and A.M. Ramalho Correia. Cham: Springer, vol. 1365, pp. 123-35.
- Brouhns, Natacha, Michel Denuit, and Ingrid Van Keilegom. 2005. Bootstrapping the Poisson Log-Bilinear Model for Mortality Forecasting. Scandinavian Actuarial Journal 3: 212-24.
- Cairns, Andrew J. G., David Blake, and Kevin Dowd. 2006. A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance 73: 687-718.
- Chetty, Raj, Michael Stepner, Sarah Abraham, Shelby Lin, Benjamin Scuderi, Nicholas Turner, Augustin Bergeron, and David Cutler. 2016. The association between income and life expectancy in the United States, 2001-2014. The Journal of the American Medical Association 315: 1750-66.
- D'Amato, Valeria, Steven Haberman, Gabriella Piscopo, Maria Russolillo, and Lorenzo Trapani. 2014. Detecting Common Longevity Trends by a Multiple Population Approach. North American Actuarial Journal 18: 139-49.
- Holzmann, Robert, and John Piggott. 2018. The Taxation of Pensions. Cambridge: MIT Press.
- Holzmann, Robert, Mercedes Ayuso, and Jorge M. Bravo. 2019. Reframing lifecycle saving and dissaving by low-, middle-, and high-income groups: Initial hypotheses, literature review, and ideas for empirical testing. In IZA Discussion Paper No. 12655. Bonn: IZA Institute of Labor Economics.
- Hunt, Andrew, and David Blake. 2021. On the structure and classification of mortality models. North American Actuarial Journal 25: S215-S234.
- Lee, Ronald D., and Lawrence R. Carter. 1992. Modeling and forecasting U.S. mortality. Journal of the American Statistical Association 87: 659-71.
- NASEM (National Academy of Sciences, Engineering and Medicine). 2015. The growing gap in life expectancy by income: Implications for federal programs and policy responses. In Committee on the Long-Run Macroeconomic Effects of the Aging U.S. Population. Washington, DC: National Academies Press. OECD. 2019. Pensions at a Glance 2019: OECD and G20 Indicators. Paris: OECD Publishing.
- Raftery, Adrian E., Tilmann Gneiting, Fadoua Balabdaoui, and Michael Polakowski. 2005. Using Bayesian Model Averaging to calibrate forecast ensembles. Journal of American Meteorological Society 133: 1155-74.
- Samuels, Jon D., and Rodrigo M. Sekkel. 2017. Model confidence sets and forecast combination. International Journal of Forecasting 33: 48-60.
- Villegas, Andrés M., Steven Haberman, Vladimir K. Kaishev, and Pietro Millossovich. 2017. A comparative study of two-population models for the assessment of basis risk in longevity hedges. ASTIN Bulletin 47: 631-79.
Cited by
Sorted by citations
Addressing the life expectancy gap in pension policy
Bravo, J. M., Ayuso, M., Holzmann, R., & Palmer, E. (2021) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2021.03.025 · Cited by 56 · see citing works
Self-citationGolpe, A. A., Fuentes, A. J. S., & Vides, J. C. (2023) · Economic Analysis and Policy · doi:10.1016/j.eap.2023.04.038 · Cited by 40 · see citing works
Intergenerational actuarial fairness when longevity increases: Amending the retirement age
Bravo, J. M., Ayuso, M., Holzmann, R., & Palmer, E. (2023) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2023.08.007 · Cited by 35 · see citing works
Self-citationModelling Motor Insurance Claim Frequency and Severity Using Gradient Boosting
Clemente, C., Guerreiro, G. R., & Bravo, J. M. (2023) · Risks · doi:10.3390/risks11090163 · Cited by 28 · see citing works
“Empirical studies show that they can provide superior predictive accuracy relative to single learners in several domain-specific areas (Ashofteh et al. 2022; Ayuso et al. 2021; Bravo 2021; Kim and Baek 2022).”
Self-citationAshofteh, A., Bravo, J. M., & Ayuso, M. (2022) · Applied Soft Computing · doi:10.1016/j.asoc.2022.109422 · Cited by 21 · see citing works
Self-citationBravo, J. M., & Ayuso, M. (2021) · Mathematics · doi:10.3390/math9243307 · Cited by 18 · see citing works
Self-citationImmunization Strategies for Funding Multiple Inflation-Linked Retirement Income Benefits
Simões, C. P. G., Oliveira, L., & Bravo, J. M. (2021) · Risks · doi:10.3390/risks9040060 · Cited by 14 · see citing works
Self-citationRegulating the retirement age—Lessons from Nordic pension policy approaches
von Nordheim, F., & Kvist, J. (2022) · Regulation & Governance · doi:10.1111/rego.12475 · Cited by 13 · see citing works
Progressive Pension Formula and Life Expectancy Heterogeneity
Diakite, K., & Devolder, P. (2021) · Risks · doi:10.3390/risks9070127 · Cited by 11 · see citing works
Life Table Forecasting in COVID-19 Times: An Ensemble Learning Approach
Ashofteh, A., & Bravo, J. M. (2021) · Iberian Conference on Information Systems and Technologies (CISTI) · doi:10.23919/cisti52073.2021.9476583 · Cited by 11 · see citing works
Self-citationForecasting Longevity for Financial Applications: A First Experiment with Deep Learning Methods
Bravo, J. M. (2021) · Communications in computer and information science · doi:10.1007/978-3-030-93733-1_17 · Cited by 10 · see citing works
Self-citationAutomobile Usage-Based-Insurance: : Improving Risk Management using Telematics Data
Cunha, L., & Bravo, J. M. (2022) · Iberian Conference on Information Systems and Technologies (CISTI) · doi:10.23919/cisti54924.2022.9820146 · Cited by 10 · see citing works
Self-citationBacktesting Recurrent Neural Networks with Gated Recurrent Unit: Probing with Chilean Mortality Data
Bravo, J. M., & Santos, V. (2022) · Lecture notes in networks and systems · doi:10.1007/978-3-030-97719-1_9 · Cited by 8 · see citing works
Self-citationShort-Term CPI Inflation Forecasting: Probing with Model Combinations
Bravo, J. M., & Mekkaoui, N. E. (2022) · Lecture notes in networks and systems · doi:10.1007/978-3-031-04826-5_56 · Cited by 8 · see citing works
Self-citationPricing Survivor Bonds with Affine-Jump Diffusion Stochastic Mortality Models
Bravo, J. M. (2021) · International Conference on E-Commerce, E-Business and E-Government (ICEEG) · doi:10.1145/3466029.3466037 · Cited by 7 · see citing works
Self-citationDrawing Down Retirement Financial Savings: A Welfare Analysis using French data
Mekkaoui, N. E., & Bravo, J. M. (2021) · International Conference on E-Commerce, E-Business and E-Government (ICEEG) · doi:10.1145/3466029.3466041 · Cited by 6 · see citing works
Self-citationAssessing the effectiveness of recent pension reforms: The French experiment
Bravo, J. M., Ayuso, M., & Mekkaoui, N. E. (2025) · Socio-Economic Planning Sciences · doi:10.1016/j.seps.2025.102335 · Cited by 5 · see citing works
Self-citationAre demographic developments undermining intergenerational compacts?
Andersen, T. M. (2025) · Journal of Population Economics · doi:10.1007/s00148-025-01138-8 · Cited by 5 · see citing works
Symeonidis, G., Tinios, P., & Chouzouris, M. (2021) · Risks · doi:10.3390/risks9110190 · Cited by 5 · see citing works
A magyar nyugdíjrendszer pontrendszerre való áttérésének vizsgálata
Banyár, J. (2023) · Közgazdasági Szemle · doi:10.18414/ksz.2023.9.964 · Cited by 4 · see citing works
Ensemble Methods for Stock Market Prediction
Bravo, J. M. (2024) · Communications in computer and information science · doi:10.1007/978-3-031-74643-7_31 · Cited by 3 · see citing works
Self-citationIndexing Pensions to Life Expectancy: Keeping the System Fair Across Generations
Ayuso, M., & Bravo, J. M. (2022) · Springer eBooks · doi:10.1007/978-3-030-99638-3_6 · Cited by 3 · see citing works
Self-citationCredit Risk Scoring: A Stacking Generalization Approach
Raimundo, B., & Bravo, J. M. (2024) · Lecture notes in networks and systems · doi:10.1007/978-3-031-45642-8_38 · Cited by 3 · see citing works
Self-citationTeixeira, J. E., Bragada, J. A. A., Bragada, J. P., Coelho, J., Sousa‐Pinto, I., Reis, L. P., & Magalhães, P. (2022) · Revista Portuguesa de Endocrinologia Diabetes e Metabolismo · doi:10.26497/ao210038 · Cited by 3 · see citing works
Dedák, I., & Fiser, N. (2023) · SSRN Electronic Journal · doi:10.2139/ssrn.4390600 · Cited by 2 · see citing works
The Riccati Tontine: How to Satisfy Regulators on AveragePreprint
Milevsky, M. A., & Salisbury, T. S. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4734668 · Cited by 2 · see citing works
Couples’ Joint Life Expectancy at Retirement Ages: Evidence from Spain
Ayuso, M., Pérez-Martí, M., & Bravo, J. M. (2025) · Springer proceedings in business and economics · doi:10.1007/978-3-031-94487-1_10 · Cited by 1 · see citing works
Self-citationMandischer, N., Füller, L., Alles, T., Flemisch, F. O., & Mikelsons, L. (2025) · Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics · doi:10.1109/smc58881.2025.11343660 · Cited by 1 · see citing works
The Demographics of Defense and Security in Japan
Bravo, J. M. (2021) · Smart innovation, systems and technologies · doi:10.1007/978-981-16-4884-7_29 · Cited by 1 · see citing works
Self-citationGradient Boosting in Motor Insurance Claim Frequency Modelling
Clemente, C., Guerreiro, G. R., & Bravo, J. M. (2023) · Conferência da Associação Portuguesa de Sistemas de Informação (CAPSI) · doi:10.18803/capsi.v23.53-69 · Cited by 1 · see citing works
Self-citationEnsemble Methods for Consumer Price Inflation Forecasting
Bravo, J. M., & Ashofteh, A. (2023) · Conferência da Associação Portuguesa de Sistemas de Informação (CAPSI) · doi:10.18803/capsi.v23.317-336 · Cited by 1 · see citing works
Self-citationPramanik, S. (2024) · Advances in finance, accounting, and economics book series · doi:10.4018/979-8-3693-2683-1.ch019 · Cited by 1 · see citing works
de Souza, F. C., Bernardino, W., & Patrício, S. C. (2024) · Journal of Population Research · doi:10.1007/s12546-024-09334-1 · Cited by 1 · see citing works
Yin, X., Xia, H., & Zheng, X. (2025) · Sustainability · doi:10.3390/su17031313 · Cited by 1 · see citing works
Milevsky, M. A. (2022) · Future of business and finance · doi:10.1007/978-3-031-00928-0_1
Financial Sustainability and the Wellbeing of the Elder Romanian Population Using Pension Modelling
Florea, N. V., Croitoru, G., Robescu, V. O., Florea, D., & Croitoru, M. B. (2024) · Advances in finance, accounting, and economics book series · doi:10.4018/979-8-3693-2881-1.ch002
Pramanik, S. (2024) · Advances in finance, accounting, and economics book series · doi:10.4018/979-8-3693-1750-1.ch001
Łyskawa, K., & Bielawska, K. (2024) · Economics and Business Review/The Poznań University of Economics Review · doi:10.18559/ebr.2024.2.1008
Financing Long-Term Care in Portugal: Is There a Role for Home Equity Release Schemes?
Bravo, J. M., & Gonçalves, J. (2025) · Springer proceedings in business and economics · doi:10.1007/978-3-031-94487-1_9
Self-citationA Stacking Generalization Approach
Raimundo, B., & Bravo, J. M. (2024) · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)
Self-citationPricing e-forwards: An Investigation Using Bayesian Model Ensembles and Stacking Regression
Bravo, J. M. (2026) · Lecture notes in networks and systems · doi:10.1007/978-3-032-12882-9_36
Self-citationCompliance risk and pension sustainability: A policy frontier approach
Tizian, D. I. C. K., Čermáková, K., Rotschedl, J., & Popescu, I. A. (2026) · Economics & Sociology · doi:10.14254/2071-789x.2026/19-1/4
Bravo, J. M., & Culotta, F. (2026) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2026.103302
Self-citationConstructing cohort life tables from incomplete data
Issahaku, I. A., & Vékás, P. (2026) · Scandinavian Actuarial Journal · doi:10.1080/03461238.2026.2724906
- Authors
- Ayuso, M., Bravo, J. M., Holzmann, R., & Palmer, E.
- Affiliations
- Universitat de Barcelona (ES)
- Centro de Estudos e Formação Avançada em Gestão e Economia (PT)
- Austrian Academy of Sciences (AT)
- Uppsala University (SE)
- Corresponding author
- Ayuso, Mercedes
- Venue
- Risks
- Publisher
- MDPI AG
- Published
- 2021-05-13
- Volume
- 9
- Issue
- 5
- Pages
- 96
- ISSN
- 2227-9091 (ISSN-L)
- OpenAlex
- W3162970916
- Cited by
- 44
- References
- 57
- Citations by year
- 2026: 4 · 2025: 6 · 2024: 9 · 2023: 7 · 2022: 8 · 2021: 10
- FWCI
- 13.39
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Risks (publishedVersion, cc-by)
- Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) (submittedVersion, other-oa)
- RePEc: Research Papers in Economics (submittedVersion)
- Dipòsit Digital de la Universitat de Barcelona (Universitat de Barcelona) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Econstor (Econstor) (submittedVersion, cc-by)
- Funders
- Ministerio de Ciencia e Innovación
- Topics
- Social Sciences › Demography › Insurance, Mortality, Demography, Risk Management
- Social Sciences › Demography › Retirement, Disability, and Employment
- Social Sciences › Business, Management and Accounting › Accounting › Financial Literacy, Pension, Retirement Analysis
- Keywords
- retirement age, life expectancy, longevity risk, pension policy, cohort life expectancy, period life expectancy, stochastic mortality models, model confidence set, policy design, Netherlands, Denmark, Portugal, Slovakia
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
