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On Mathematical Models of Extreme Values Probabilities Mixtures


  • Shchetinin, Eugene
  • Nazarenko, Kirill


A new mathematical model of extreme values probability mixture is proposed in the paper. Effective computational algorithms for modeling probability mixture and value at risk (VaR) capital estimation are developed and rigorously proved. Comparative analysis of VaR-estimation with threshold and mixture models based on the Dow Jones historical data (01.01.1950 – 10.08.2005) has shown a high effectiveness of the last one for risk capital estimation of an issuing company

Suggested Citation

  • Shchetinin, Eugene & Nazarenko, Kirill, 2007. "On Mathematical Models of Extreme Values Probabilities Mixtures," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 7(3), pages 44-52.
  • Handle: RePEc:ris:apltrx:0141

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    References listed on IDEAS

    1. Ying Chen & Wolfgang Härdle & Vladimir Spokoiny, 2005. "Portfolio Value at Risk Based on Independent Components Analysis," SFB 649 Discussion Papers SFB649DP2005-060, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Robert F. Engle & Simone Manganelli, 1999. "CAViaR: Conditional Value at Risk by Quantile Regression," NBER Working Papers 7341, National Bureau of Economic Research, Inc.
    3. I. D. Vrontos & P. Dellaportas & D. N. Politis, 2003. "A full-factor multivariate GARCH model," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 312-334, December.
    4. Giamouridis, Daniel & Vrontos, Ioannis D., 2007. "Hedge fund portfolio construction: A comparison of static and dynamic approaches," Journal of Banking & Finance, Elsevier, vol. 31(1), pages 199-217, January.
    5. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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    More about this item


    VaR; risk capital estimation;

    JEL classification:

    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • O13 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Agriculture; Natural Resources; Environment; Other Primary Products
    • Q32 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - Exhaustible Resources and Economic Development


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