IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-02935500.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Terraza, M., 2014. "Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns," Economic Modelling, Elsevier, vol. 39(C), pages 247-256.
    2. Jules Sadefo Kamdem, 2012. "VaR and ES for linear portfolios with mixture of generalized Laplace distributions risk factors," Annals of Finance, Springer, vol. 8(1), pages 123-150, February.
    3. Abdoul Salam Diallo & Alfred Mbairadjim Moussa, 2014. "Addressing agent specific extreme price risk in the presence of heterogeneous data sources: A food safety perspective," Working Papers 14-15, LAMETA, Universtiy of Montpellier, revised Dec 2014.
    4. 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.
    5. Raymond BRUMMELHUIS & Jules Sadefo-Kamdem, 2009. "Var For Quadratic Portfolio'S With Generalized Laplace Distributed Returns," Working Papers 09-06, LAMETA, Universtiy of Montpellier, revised Jun 2009.
    6. 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.
    7. Jules Sadefo Kamdem & Zoulkiflou Moumouni, 2020. "Comparison of Some Static Hedging Models of Agricultural Commodities Price Uncertainty," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(3), pages 631-655, September.
    8. 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.
    9. Zoulkiflou Moumouni & Jules Sadefo-Kamdem, 2019. "New models of commodity risk hedging according to the behavior of economic decision-makers or Rollover Strategies," Working Papers hal-02417459, HAL.
    10. Christensen, Kim & Oomen, Roel C.A. & Podolskij, Mark, 2014. "Fact or friction: Jumps at ultra high frequency," Journal of Financial Economics, Elsevier, vol. 114(3), pages 576-599.
    11. Glasserman, Paul & Kim, Kyoung-Kuk, 2009. "Saddlepoint approximations for affine jump-diffusion models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 15-36, January.
    12. Stelios Bekiros & Nikolaos Loukeris & Iordanis Eleftheriadis & Christos Avdoulas, 2019. "Tail-Related Risk Measurement and Forecasting in Equity Markets," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 783-816, February.
    13. Jules Sadefo-Kamdem, 2011. "Downside Risk And Kappa Index Of Non-Gaussian Portfolio With Lpm," Working Papers hal-00733043, HAL.
    14. Breuer, Thomas & Jandacka, Martin & Rheinberger, Klaus & Summer, Martin, 2010. "Does adding up of economic capital for market- and credit risk amount to conservative risk assessment?," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 703-712, April.
    15. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2015. "Risk Estimation via Regression," Operations Research, INFORMS, vol. 63(5), pages 1077-1097, October.
    16. J. Christopher Westland, 2015. "Economics of eBay’s buyer protection plan," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 1(1), pages 1-20, December.
    17. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    18. Thai Nguyen, 2016. "Optimal investment and consumption with downside risk constraint in jump-diffusion models," Papers 1604.05584, arXiv.org.
    19. Taamouti, Abderrahim, 2009. "Analytical Value-at-Risk and Expected Shortfall under regime-switching," Finance Research Letters, Elsevier, vol. 6(3), pages 138-151, September.
    20. Arismendi, Juan C. & Broda, Simon, 2017. "Multivariate elliptical truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 29-44.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-02935500. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.