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Sharp estimates for the CDF of quadratic forms of MPE random vectors

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  • J. Sadefo Kamdem

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

Abstract

n this paper we develop an efficient analytical expansion of the cumulative distribution function (cdf) XBX^t where X=(X"1,...,X"n"+"1) with n>=2, follows a multivariate power exponential distribution (MPE). Our approach provides a sharp estimate of the cumulative distribution function of a quadratic form of MPE, together with explicit error estimates.

Suggested Citation

  • J. Sadefo Kamdem, 2010. "Sharp estimates for the CDF of quadratic forms of MPE random vectors," Post-Print hal-02935500, HAL.
    • Handle: RePEc:hal:journl:hal-02935500
    DOI: 10.1016/J.JMVA.2010.03.002
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    References listed on IDEAS

    as
    1. Sadefo Kamdem, J. & Genz, A., 2008. "Approximation of multiple integrals over hyperboloids with application to a quadratic portfolio with options," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3389-3407, March.
    2. Jun Pan & Darrell Duffie, 2001. "Analytical value-at-risk with jumps and credit risk," Finance and Stochastics, Springer, vol. 5(2), pages 155-180.
    3. Jules Sadefo Kamdem, 2005. "Value-At-Risk And Expected Shortfall For Linear Portfolios With Elliptically Distributed Risk Factors," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(05), pages 537-551.
    4. Jaschke, Stefan & Klüppelberg, Claudia & Lindner, Alexander, 2004. "Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 252-273, February.
    5. Sadefo Kamdem, J., 2009. "[Delta]-VaR and [Delta]-TVaR for portfolios with mixture of elliptic distributions risk factors and DCC," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 325-336, June.
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    Cited by:

    1. Dobrislav Dobrev∗ & Travis D. Nesmith & Dong Hwan Oh, 2017. "Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors," JRFM, MDPI, vol. 10(1), pages 1-14, February.

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