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2021 | 22 | nr 3 | 31--57
Tytuł artykułu

The Complex-Number Mortality Model (CNMM) Based on Orthonormal Expansion of Membership Functions

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper deals with a new fuzzy version of the Lee-Carter (LC) mortality model, in which mortality rates as well as parameters of the LC model are treated as triangular fuzzy numbers. As a starting point, the fuzzy Koissi-Shapiro (KS) approach is recalled. Based on this approach, a new fuzzy mortality model - CNMM - is formulated using orthonormal expansions of the inverse exponential membership functions of the model components. The paper includes numerical findings based on a case study with the use of the new mortality model compared to the results obtained with the standard LC model.(original abstract)
Rocznik
Tom
22
Numer
Strony
31--57
Opis fizyczny
Twórcy
  • University of Lodz, Poland
  • University of Lodz, Poland
Bibliografia
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  • Danesi, I. L., Haberman, S., Millossovich, P., (2015). Forecasting mortality in subpopulations using Lee-Carter type models: A comparison, Insurance: Mathematics and Economics, 62(4), pp. 151-161.
  • De Jong, P., Tickle, L., (2006). Extending Lee-Carter mortality forecasting. Mathematical Population Studies, 13(1), pp. 1-18.
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  • Ishikawa, S., (1997). Fuzzy inferences by algebraic method, Fuzzy Sets and Systems, 87, pp. 181-200.
  • Koissi, M.-C., Shapiro, A. F., (2006). Fuzzy formulation of the Lee-Carter model for mortality forecasting, Insurance: Mathematics and Economics, 39, pp. 287-309.
  • Kosiński, W., Prokopowicz, P., Ślęzak, D., (2003). Ordered Fuzzy Numbers, Bull. Polish Acad. Sci. Math., 51, pp. 327-338.
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  • Pitacco, E., Denuit, M., Haberman, S., Olivieri, A., (2009). Modelling Longevity Dynamics for Pensions and Annnuity Business, Oxford University Press.
  • Prokopowicz, P., Czerniak, J., Mikołajewski, D., Apiecionek, Ł., Ślęzak, D. (eds.), (2017). Ordered Fuzzy Numbers: Definitions and Operations, Studies in Fuzziness and Soft Computing, vol. 356, Springer Open.
  • Renshaw, A. E., Haberman, S., (2003). Lee-Carter mortality forecasting with age specific enhancement, Insurance: Mathematics and Economics, 33(2), pp. 255-272.
  • Renshaw, A., Haberman, S., Hatzopoulos, P., (1996). The modelling of recent mortality trends in United Kingdom male assured lives. British Actuarial Journal, 2, pp. 449-477.
  • Rossa, A., Socha, L., Szymański, A., (2011). Analiza i modelowanie umieralności w ujęciu dynamicznym (in Polish), University of Lodz Press, Łódź.
  • Rossa, A., Socha, L., Szymański, A., (2017). Hybrid Dynamic and Fuzzy Models of Mortality. University of Lodz Press.
  • Szymański, A., Rossa, A., (2014). Fuzzy mortality model based on Banach algebra, International Journal of Intelligent Technologies and Applied Statistics, 7,pp. 241-265.
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
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