Sharp estimates for the CDF of quadratic forms of MPE random vectors
In this paper we develop an efficient analytical expansion of the cumulative distribution function (cdf) where 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.
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Volume (Year): 101 (2010)
Issue (Month): 8 (September)
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- 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.
- 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.
- 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.
- Jun Pan & Darrell Duffie, 2001. "Analytical value-at-risk with jumps and credit risk," Finance and Stochastics, Springer, vol. 5(2), pages 155-180.
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