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2018 | OriginalPaper | Buchkapitel

Mortality Rates Smoothing Using Mixture Function

verfasst von : Samuel Hudec, Jana Špirková

Erschienen in: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations

Verlag: Springer International Publishing

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Abstract

The paper offers a description of the new method of a smoothing of the mortality rates using the so-called moving mixture functions. Mixture functions represent a special class of weighted averaging functions where weights are determined by continuous, input values dependent, weighting functions. If they are increasing, they form an important class of aggregation functions. Such mixture functions are more flexible than the standard weighted arithmetic mean, and their weighting functions allow one to penalize or reinforce inputs based on their magnitude. The advantages of this method are that the weights of the input values depend on ourselves and coefficients of weighting functions can be changed each year so that the mean square error is minimized. Moreover, the paper offers the impact of this method on the amount of whole life pension annuities.

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Vorheriges Kapitel Mapping Utilities to Transitive Preferences

Nächstes Kapitel Aggregation Functions Based on Deviations

The term “increasing” is understood in a non-strict sense.

Council Directive 2004/113/EC, Under new rules which are entering into force, insurers in Europe will have to charge the same prices to women and men for the same insurance products without distinction on the grounds of sex.

Directive 2009/138/EC of the European Parliament and of the Council of 25 November 2009 on the taking-up and pursuit of the business of Insurance and Reinsurance (Solvency II).

Beliakov, G., Bustince Sola, H., Calvo Sánchez, T.: A Practical Guide to Averaging Functions. Studies in Fuzziness and Soft Computing, vol. 329. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-24753-3CrossRef

Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. Springer, Berlin (2007). https://doi.org/10.1007/978-3-540-73721-6CrossRefMATH

Beliakov, G., Calvo, T., Wilkin, T.: Three types of monotonicity of averaging functions. Knowl.-Based Syst. 72, 114–122 (2014)CrossRef

Beliakov, G., Calvo, T., Wilkin, T.: On the weak monotonicity of Gini means and other mixture functions. Inf. Sci. 300, 70–84 (2015)MathSciNetCrossRef

Beliakov, G., Špirková, J.: Weak monotonicity of Lehmer and Gini means. Fuzzy Sets Syst. 299, 26–40 (2016)MathSciNetCrossRef

Bustince, H., Fernandez, J., Kolesárová, A., Mesiar, R.: Fusion functions and directional monotonicity. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2014. CCIS, vol. 444, pp. 262–268. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08852-5_27CrossRef

Currie, I.D., Durban, M., Eilers, P.H.C.: Smoothing and forecasting mortality rates. Stat. Model. 4, 279 (2004). https://doi.org/10.1191/1471082X04st080oa. http://www.maths.ed.ac.uk/~mthdat25/mortality/Smoothing-and-forecasting-mortality-rates.pdfMathSciNetCrossRef

Dickson, D.C.M., et al.: Actuarial Mathematics for Life Contingent Risks. Cambridge University Press, New York (2009)CrossRef

Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)CrossRef

10.

Euro area yield curves. https://www.ecb.europa.eu/stats/financial_markets_and_interest_rates/euro_area_yield_curves/html/index.en.html

11.

Hunt, A., Blake, D.: Modelling mortality for pension schemes. ASTIN Bull. 47(2), 601–629 (2017)MathSciNetCrossRef

12.

The Human Mortality Database. https://mortality.org/

13.

James, G., Witten, D., Hastie, T., Tibshirani, R.: An Introduction to Statistical Learning with Applications in R. Springer, New York (2013). https://doi.org/10.1007/978-1-4614-7138-7CrossRefMATH

14.

Lee, R.D., Carter, L.R.: Modeling and forecasting U. S. mortality. J. Am. Stat. Assoc. 87(419), 659–671 (1992). http://pagesperso.univ-brest.fr/~ailliot/doc_cours/M1EURIA/regression/leecarter.pdf

15.

Marková, V., Lesníková, P., Kaščáková, A., Vinczeová, M.: The present status of sustainability concept implementation by businesses in selected industries in the Slovak Republic. E&M Econ. Manag. 20(3), 101–117 (2017). https://doi.org/10.15240/tul/001/2017-3-007CrossRef

16.

Mesiar, R., Špirková, J.: Weighted means and weighting functions. Kybernetika 42(2), 151–160 (2006)MathSciNetMATH

17.

Mesiar, M., Špirková, J., Vavríková, L.: Weighted aggregation operators based on minimization. Inf. Sci. 17(4), 1133–1140 (2008)MathSciNetCrossRef

18.

Nakazawa, M.: Package ‘fmsb’. https://cran.r-project.org/web/packages/fmsb/fmsb.pdf

19.

Potocký, R.: Models in life and non-life insurance. In: Slovak: Modely v životnom a neživotnom poistení, Bratislava, STATIS (2012)

20.

R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/

21.

Richards, S.J.: Detecting year-of-birth mortality patterns with limited data. J. R. Stat. Soc. Ser. Stat. Soc. 171(Part: 1), 279–298 (2008)MathSciNet

22.

Statistical Office of the Slovak Republic. https://slovak.statistics.sk/

23.

Szűcs, G., Špirková, J., Kollár, I.: Detailed View of a Payout Product of the Old-Age Pension Saving Scheme in Slovakia. J. Econ. (2018, submitted). Institute of Economic Research SAS, Slovakia

24.

Špirková, J.: Dissertation thesis. In: Weighted Aggregation Operators and Their Applications, Bratislava (2008)

25.

Špirková, J.: Weighted operators based on dissimilarity function. Inf. Sci. 281, 172–181 (2014)MathSciNetCrossRef

26.

Špirková, J.: Induced weighted operators based on dissimilarity functions. Inf. Sci. 294, 530–539 (2015)MathSciNetCrossRef

27.

Vinczeová, M.: The relationship between corporate social responsibility and business performance (in Slovak: Vzt’ah medzi spoločenskou zodpovednost’ou podniku a jeho výkonnost’ou). In: Proceedings of Scientific Studies from the Project VEGA No. 1/0934/16 Cultural Intelligence as an Important Presumption of Slovakia’s Competitiveness in a Global Environment (in Slovak: Zborník vedeckých štúdií z projektu VEGA 1/0934/16 Kultúrna inteligencia ako d\(\hat{o}\)ležitý predpoklad konkurencieschopnosti Slovenska v globálnom prostredí). Faculty of Economics, Matej Bel Univerzity, CD-ROM, Banská Bystrica (2016)

28.

Wickham, H.: ggplot2 Elegant Graphics for Data Analysis, 2nd edn. Springer, New York (2016). https://doi.org/10.1007/978-3-319-24277-4CrossRefMATH

29.

Zimmermann, P.: Modeling mortality at old age with time-varying parameters. Math. Popul. Stud. 24(3), 172–180 (2017). https://doi.org/10.1080/08898480.2017.1330013MathSciNetCrossRef

Titel: Mortality Rates Smoothing Using Mixture Function
verfasst von: Samuel Hudec
Jana Špirková
Verlag: Springer International Publishing
Buch: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations
Print ISBN: 978-3-319-91472-5

Electronic ISBN: 978-3-319-91473-2

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-91473-2_12

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