Simplified Azbel model to adjust Peruvian mortality tables for pension purposes
DOI:
https://doi.org/10.21754/iecos.v24i1.1592Keywords:
Simplified Azbel model, similarity measures, mortality adjustment, life tablesAbstract
In this research, the Simplified Azbel model was estimated to verify that it is a good fit to mortality rates for pension purposes in Peru, using three estimation methods, maximum likelihood (MV), log-linear regression-type method and ordinary least squares (OLS) method. The mortality tables were segmented into three age groups. It was confirmed that there is a difference in the fit between men and women. With the A/E and ARL similarity metrics, the original and the estimated mortality tables, the hypothesis is corroborated since it is concluded that the best estimates resulted for the SP2005 tables, for the male gender with the Log-linear Regression-type and ordinary least squares methods, except for the range between 50 and 90 years of age. In women, there is only a good fit with the Log-linear Regression-type method from 15 years of age onwards. The fit to the SPP2017 tables is barely noticeable in men with the Log-linear Regression-type method from the age of 70 years and in women from the age of 80 years.
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References
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Andreeski, C. (2013). Optimal Values for Calculation of Premium in Life Insurance. (I. Global, Ed.) International Journal of Energy Optimization and Engineering (IJEOE), 2(3), 68-85. https://doi.org/10.4018/ijeoe.2013070105
Andreeski, C. J., & Topuzoska, S. (2016). Structural analysis of life insurance: A comparative study between the Republic of Macedonia and Republic of Serbia. Civitas, 6(2), 24-34. https://doi.org/10.5937/Civitas1602024A
Andreeski, C. J., & Vasant, P. (2008, July). Simplified Azbel Model for Fitting Mortality Tables. Proceedings of the 17th World Congress The International Federation of Automatic Control, 41(2), 2980-2983. https://doi.org/10.3182/20080706-5-KR-1001.00501
Arató, M., Bozsó, D., Elek, P., & Zempléni, A. (2009). Forecasting and simulating mortality tables. Mathematical and Computer Modelling, 49(3-4), 805-813. https://doi.org/10.1016/j.mcm.2008.01.012
Azbel, M. Y. (1996). Unitary Mortality Law and Species-Specific Age. Proceedings of the Royal Society of London. Series B: Biological Sciences, 263(1376), 1449-1454. https://doi.org/10.1098/rspb.1996.0211
Azbel, M. Y. (1997). Phenomenological theory of mortality. Physics reports, 288(1-6), 545-574. https://doi.org/10.1016/S0370-1573(97)00040-9
Azbel, M. Y. (1999). Empirical laws of survival and evolution: Their universality and implications. Proceedings of the National Academy of Sciences, 96(26), 15368-15373. https://doi.org/10.1073/pnas.96.26.15368
Azbel, M. Y. (2002). Law of universal mortality. Physical Review E, 66(1), 016107. https://doi.org/10.1103/PhysRevE.66.016107
Azbel, M. Y. (2002). The law of invariante mortality. Physica A: Statistical Mechanics and its Applications, 310(3-4), 501-508. https://doi.org/10.1016/S0378-4371(02)00735-5
Bacaër, N. (2011). Halley’s life table (1693). A Short History of Mathematical Population Dynamics, 5-10. https://doi.org/10.1007/978-0-85729-115-8_2
Bergeron Boucher, M.-P., Kjaergaard, S., Oeppen, J., & Vaupel, J. W. (2019). The impact of the choice of life table statistics when forecasting mortality. Demographic Research, 41(43), 1235-1268. https://doi.org/10.4054/DemRes.2019.41.43
Booth, H., & Tickle, L. (2008). Mortality Modelling and Forecasting: A Review of Methods. Annals of Actuarial Sciences, 3(1-2), 3-43.
https://doi.org/10.1017/s1748499500000440
Cerda Hernandez, J. J., & Sikov, A. (2021). Lee-Carter method for forecasting mortality for Peruvian Population. Selecciones Matemáticas, 8(1), 52-65.
https://doi.org/10.17268/sel.mat.2021.01.05
De Oliveira, P. C., Moss de Oliveira, S., & Stauffer, D. (1999). Evolution, Money, War, and Computers. https://link.springer.com/book/10.1007/978-3-322-91009-7
Decreto Ley N. °19990 de 1973 [Ministerio de Economía y Finanzas]. Se crea el Sistema Nacional de Pensiones de la Seguridad Social. 30 de abril de 1973.
Heligman, L., & Pollard, J. H. (1980). The Age Pattern of Mortality. Journal of The Institute of Actuaries, 107(01), 49-80. https://doi.org/10.1017/S0020268100040257
Mitchell, O. S., & McCarthy, D. (2002). Estimating international adverse selection in annuities. North American Actuarial Journal, 6(4), 38-54.
https://doi.org/10.1080/10920277.2002.10596062
Racco, A., Argollo de Menezes , M., & Penna, T. (2021). Search for an unitary mortality law through a theoretical model for biological ageing. Arxiv.
https://doi.org/10.48550/arXiv.adap-org/9709002
Resolución Ministerial N.° 146-2007-EF/15 de 2007 [Ministerio de Economía y Finanzas]. Sustituyen Anexo de la R.M. Nº 757-2006-EF/15 que aprobó la Tabla de Mortalidad “Sistema Previsional - SP 2005”. 23 de marzo de 2007.
Resolución Ministerial N. º 757-2006-EF/15 de 2006 [Ministerio de Economía y Finanzas]. Aprueban Tabla de Mortalidad SP 2005. 27 de diciembre de 2006.
Resolución Suprema N. ° 002-2006-EF de 2006 [Ministerio de Economía y Finanzas]. Aceptan Cooperación Técnica No Reembolsable otorgada por la CAF, destinada al Proyecto "Elaboración de Tablas de Mortalidad en Perú". 13 de enero de 2006.
Richmond, P., Roehner, B. M., Irannezhad, A., & Hutzler, S. (2021). Mortality: A physics perspective. Physica A: Statistical Mechanics and its Applications, 566, 125660. https://doi.org/10.1016/j.physa.2020.125660
Tehrani, R., Najjarpour, A., & Soltani, M. (2017). Prediction and Simulation of Mortality Tables in Iran. International Journal of Economic Perspectives, 11(2), 218-224. https://www.proquest.com/scholarly-journals/prediction-simulation-mortality-tables-iran/docview/2038224269/se-2
Published
2023-08-11
How to Cite
Infante Rojas, M. D., Benito Santillán, A. F., Campos Palpa, G. E., & Huapaya Caycho, A. E. (2023). Simplified Azbel model to adjust Peruvian mortality tables for pension purposes. Revista IECOS, 24(1), 74–101. https://doi.org/10.21754/iecos.v24i1.1592
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