Using Parametric Bootstrap to Introduce and Manage Uncertainty: Replicated Loaded Insurance Life Tables

References

• American Academy of Actuaries. 2002. Report of the American Academy of Actuaries’ Commissioners Standard Ordinary Task Force, paper presented at the National Association of Insurance Commissioners’ Life and Health Actuarial Task Force. Philadelphia, June.
   Google Scholar
• American Academy of Actuaries. 2015. Report on the 2017 CSO and 2017 CSO Preferred Structure Table Development. October. https://www.soa.org/Files/Research/Exp-Study/research-2017-cso-report.pdf.
   Google Scholar
• American Academy of Actuaries. 2018. The Pension Protection Act: Successes, shortcomings, and opportunities for improvement. April. https://www.actuary.org/content/pension-protection-act-successes-shortcomings-and-opportunities-improvement-0.
   Google Scholar
• Ayuso, M., H. Corrales, M. Guillén, A. M. Pérez‐Marín, and J. L. Rojo. 2007. Estadística actuarial vida. Barcelona: Edicions Universitat de Barcelona.
   Google Scholar
• Beer, J. 2000. Dealing with uncertainty in population forecasting. Statistics Netherlands, 1–40.
   Google Scholar
• Benjamin, B., and J. H. Pollard. 1993. The Analysis of Mortality and other Actuarial Statistics. Oxford: Institute of Actuaries and the Faculty of Actuaries.
   Google Scholar
• Bijak, J., E. Dodd, J. J. Forster, and P. W. F. Smith. 2015. Smoothing mortality data: Producing the English life table, 2010–12. English Life Tables: 17 Methodology, 1–18.
   Google Scholar
• Blätter DGVFM. 2009. Herleitung der Sterbetafel DAV 2008 T für Lebensversicherungen mit Todesfallcharakter. DAV-Unterarbeitsgruppe Todesfallrisiko 30: 189–224. doi:10.1007/s11857-009-0076-4.
   Google Scholar
• Boletín Oficial del Estado. 2012. 4 Dirección General del Seguro y Fondos de Pensiones. Resolución del 6 de julio de 2012, 2012-07-21. BOE, 174, Sec. I., 52491.
   Google Scholar
• Brouhns, N., and M. Denuit. 2002. Risque de longévité et rentes viagères II. Tables de mortalitè prospectives pour la population belge. Belgian Actuarial Bulletin 2 (1): 50–63.
   Google Scholar
• Brouhns, N., M. Denuit, and I. V. Keilegom. 2005. Bootstrapping the Poisson log-bilinear model for mortality forecasting. Scandinavian Actuarial Journal 3: 212–24.
   Google Scholar
• Brouhns, N., M. Denuit, and J. K. Vermunt. 2002a. A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics & Economics 31 (3): 373–93.
   Web of Science ®Google Scholar
• Brouhns, N., M. Denuit, and J. K. Vermunt, 2002b, Measuring the longevity risk in mortality projections. Bulletin of the Swiss Association of Actuaries, 105–30.
   Google Scholar
• Chernick, M. R. 2008. Bootstrap methods: A Guide for Practitioners and Researchers. Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• Chiang, C. L. 1984. The Life Tables and its Applications. Malabar, FL: R. E. Krieger.
   Google Scholar
• Copas, J. B., and S. Haberman. 1983. Non-parametric graduation using kernel methods. Journal of the Institute of Actuaries 110 (1): 135–56.
   Google Scholar
• D’Amato, V., S. Haberman, G. Piscopo, and M. Russolillo. 2012. Modelling dependent data for longevity projections. Insurance: Mathematics and Economics 51: 694–701.
   Web of Science ®Google Scholar
• Debón, A., F. Montes, and F. Puig. 2008. Modelling and forecasting mortality in Spain. European Journal of Operational Research 189 (3): 624–37.
   Web of Science ®Google Scholar
• Debón, A., F. Montes, and R. Sala. 2005. A comparison of parametric models for mortality graduation. Application to mortality data for the Valencia Region (Spain). SORT: Statistics and Operation Research Transitions 29 (2): 269–88.
   Google Scholar
• Debón, A., F. Montes, and R. Sala. 2006. A comparison of models for dynamic life tables. Application to mortality data from the Valencia Region (Spain). Lifetime Data Analysis 12 (2): 223–44.
   PubMed Web of Science ®Google Scholar
• Delwarde, A., M. Denuit, and C. Partrat. 2007. Negative binomial version of the Lee–Carter model for mortality forecasting. Applied Stochastic Models in Business and Industry 23: 385–401.
   Web of Science ®Google Scholar
• Efron, B., and R. Tibshirani. 1993. An Introduction to the Bootstrap. London: Chapman & Hall/CRC.
   Google Scholar
• Forfar, D. O., M. A. McCutcheon, and M. A. Wilkie. 1988. On graduation by mathematical formula. Journal of the Institute of Actuaries 115 (I): 1–149.
   Google Scholar
• Gaille, S., and M. Sherris. 2011. Modelling mortality with common stochastic long-run trends. Geneva Papers on Risk and Insurance—Issues and Practice 36: 595–621.
   Web of Science ®Google Scholar
• Garg, M. L., R. B. Rao, and C. K. Redmond. 1970. Maximum-likelihood estimation of the parameters of the Gompertz survival function. Journal of the Royal Statistical Society: Series C (Applied Statistics) 19 (2): 152–59.
   Web of Science ®Google Scholar
• Gavin, J., S. Haberman, and R. Verrall. 1993. Moving weighted average graduation using kernel estimation. Insurance: Mathematics and Economics 12: 113–26.
   Web of Science ®Google Scholar
• Gavin, J., S. Haberman, and R. Verrall. 1994. On the choice of bandwidth for kernel graduation. Journal of the Institute of Actuaries 121 (1): 119–34.
   Google Scholar
• Grothendieck, G. 2013. nls2: Non-linear regression with brute force. R package version 0.2. https://CRAN.R-project.org/package=nls2.
   Google Scholar
• Haberman, S., and A. Renshaw. 2009. On age-period-cohort parametric mortality rate projections. Insurance: Mathematics and Economics 45: 255–70.
   Web of Science ®Google Scholar
• Han, P. K. J., W. Klein, and K. A. Neeraj. 2011. Varieties of uncertainty in health care: A conceptual taxonomy. Medical Decision Making 31: 828–38.
   PubMed Web of Science ®Google Scholar
• Helligman, L. M. A., and J. H. Pollard. 1980. The age pattern of mortality. Journal of the Institute of Actuaries 107 (I): 49–82.
   Google Scholar
• Hernandez-Flores, C. N., J. Artiles-Romero, and P. Saavedra-Santana. 1999. Estimation of the population spectrum with replicated time series. Computational Statistics & Data Analysis 30 (3): 271–80.
   Web of Science ®Google Scholar
• Human Mortality Database. 2013. University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). www.mortality.org and www.humanmortality.de.
   Google Scholar
• ICEA. 2012. Investigación Cooperativa entre Entidades Aseguradoras y Fondos de Pensiones. Tablas de Mortalidad de la Población Asegurada Española PASEM 2010. http://www.icea.es.
   Google Scholar
• Karlis, D., and A. Kostaki. 2002. Bootstrap techniques for mortality models. Biometrical Journal 44 (7): 850–66.
   Web of Science ®Google Scholar
• Koissi, M. C., A. F. Shapiro, and G. Högnäs. 2006. Evaluating and extending the Lee–Carter model for mortality forecasting: Bootstrap confidence interval. Insurance: Mathematics and Economics 38: 1–20.
   Web of Science ®Google Scholar
• Lazar, D., and M. M. Denuit. 2009. A multivariate time series approach to projected life tables. Applied Stochastic Models in Business and Industry 25: 806–23.
   Web of Science ®Google Scholar
• Lee, R., and L. Carter. 1992. Modelling and forecasting U.S. mortality. Journal of the American Statistical Association 87: 659–71.
   Web of Science ®Google Scholar
• Li, H., and Y. Lu. 2018. A Bayesian non-parametric model for small population mortality. Scandinavian Actuarial Journal 2018 (7): 605–28.
   Google Scholar
• Lledó, J., J. M. Pavía, and F. G. Morillas. 2017. Assessing implicit hypothesis in life table construction. Scandinavian Actuarial Journal 2017 (6): 495–518.
   Web of Science ®Google Scholar
• Lledó, J., J. M. Pavía, and F. G. Morillas. 2018. The level of mortality in insured populations, in Mathematical and Statistical Methods for Actuarial Sciences and Finance, ed. M. Corazza et al., 449–54. New York: Springer.
   Google Scholar
• Nocon, A. S., and W. F. Scott. 2011. An extension of the Whittaker-Henderson method of graduation. Scandinavian Actuarial Journal 2011: 70–79.
   Google Scholar
• Pavía, J. M. 2015. Testing goodness-of-fit with the kernel density estimator: GoFKernel, Journal of Statistical Software 66 (CS1): 1–27.
   Web of Science ®Google Scholar
• Pavía Miralles, J. M., and R. Escuder Vallés. 2003. El proceso estocástico de muerte. Diferentes estrategias para la elaboración de tablas recargadas. Análisis de sensibilidad. Estadística Española 153: 253–74.
   Google Scholar
• Prieto, E., and M. J. Fernández. 1994. Tablas de mortalidad de la población española de 1950 a 1990. Tabla proyectada del año 2000. Madrid: UNESPA.
   Google Scholar
• R Core Team. 2013. R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing. http://www.R-project.org.
   Google Scholar
• Ramlau-Hansen, H. 1983. Smoothing counting process intensities by means of kernel functions. Annals of Statistics 11 (2): 453–66.
   Web of Science ®Google Scholar
• Regan, H. M., M. Colyvan, and M. A. Burgman. 2002. A taxonomy and treatment of uncertainty for ecology and conservation biology. Ecological Society of America 12 (2): 618–28.2.0.CO;2]
   Google Scholar
• Rempala, G. A., and K. Szatzschneider. 2004. Bootstrapping parametric models of mortality. Scandinavian Actuarial Journal 2004: 53–78.
   Google Scholar
• Renshaw, A. E., S. Haberman, and P. Hatzopoulos. (1996). The modelling of recent mortality trends in United Kingdom male assured lives. British Actuarial Journal 2 (2): 449–77.
   Google Scholar
• Renshaw, A. E., S. Haberman, and P. Hatzapoulos. 1997. On the duality of assumptions underpinning the construction of life tables. ASTIN Bulletin 27 (1): 5–22.
   Google Scholar
• Sakamoto, Y., M. Ishiguro, and G. Kitagawa. 1986. Akaike Information Criterion Statistics. Dordrecht: D. Reidel.
   Google Scholar
• Sithole, T. Z., S. Haberman, and R. J. Verrall. 2000. An investigation into parametric models for mortality projections, with applications to immediate annuitants’ and life office pensioners’ data. Insurance: Mathematics and Economics 27 (3): 285–312.
   Web of Science ®Google Scholar
• Su, S., and M. Sherris. 2012. Heterogeneity of Australian population mortality and implications for a viable life annuity market. Insurance: Mathematics and Economics 51: 322–32.
   Web of Science ®Google Scholar
• Villegas, A. M., and S. Haberman. 2014. On the modeling and forecasting of socioeconomic mortality differentials: An application to deprivation and mortality in England. North American Actuarial Journal 18 (1): 168–93.
   Google Scholar
• Wong-Fupuy, C., and S. Haberman. 2004. Projecting mortality trends: Recent developments in the United Kingdom and the United States. North American Actuarial Journal 8 (2): 56–83.
   Google Scholar