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On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

Listed author(s):
  • Bernhart German
  • Scherer Matthias

    (Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany)

  • Mai Jan-Frederik

    (XAIA Investment GmbH, Sonnenstraße 19, 80331 München, Germany)

Registered author(s):

    Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choicewhen modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper develops new parametric families of MSMVE distributions in arbitrary dimensions. Furthermore, a convenient stochastic representation is stated for such models, which is helpful with regard to sampling strategies.

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    Article provided by De Gruyter Open in its journal Dependence Modeling.

    Volume (Year): 3 (2015)
    Issue (Month): 1 (May)
    Pages: 1-18

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    Handle: RePEc:vrs:demode:v:3:y:2015:i:1:p:18:n:3
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    1. François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
    2. Joe, Harry, 1990. "Families of min-stable multivariate exponential and multivariate extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 9(1), pages 75-81, January.
    3. Ressel, Paul, 2013. "Homogeneous distributions—And a spectral representation of classical mean values and stable tail dependence functions," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 246-256.
    4. F. Ballani & M. Schlather, 2011. "A construction principle for multivariate extreme value distributions," Biometrika, Biometrika Trust, vol. 98(3), pages 633-645.
    5. Jiménez, Javier Rojo & Villa-Diharce, Enrique & Flores, Miguel, 2001. "Nonparametric Estimation of the Dependence Function in Bivariate Extreme Value Distributions," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 159-191, February.
    6. Ser-Huang Poon, 2004. "Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications," Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 581-610.
    7. Anne-Laure Fougères & John P. Nolan & Holger Rootzén, 2009. "Models for Dependent Extremes Using Stable Mixtures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 42-59.
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