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Extreme dependence for multivariate data

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  • Alfred Galichon

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Damien Bosc

Abstract

We present a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the cross-covariance matrices, we also generalize the notion of positive upper dependence. We then quantify the strength of dependence between two given multivariate series using an entropic distance to extremally dependent distributions. We apply this method to build indices of exposure to a financial environment, and to do stress-tests on the correlation between two sets of financial variables.

Suggested Citation

  • Alfred Galichon & Damien Bosc, 2010. "Extreme dependence for multivariate data," Working Papers hal-03588294, HAL.
  • Handle: RePEc:hal:wpaper:hal-03588294
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03588294
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    References listed on IDEAS

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    1. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0p30p95 is not listed on IDEAS
    2. Carlier, G. & Dana, R.-A. & Galichon, A., 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," Journal of Economic Theory, Elsevier, vol. 147(1), pages 207-229.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Arnaud Dupuy & Alfred Galichon, 2014. "Personality Traits and the Marriage Market," Journal of Political Economy, University of Chicago Press, vol. 122(6), pages 1271-1319.
    5. repec:dau:papers:123456789/9713 is not listed on IDEAS
    6. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    7. repec:dau:papers:123456789/2278 is not listed on IDEAS
    8. Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
    9. repec:hal:spmain:info:hdl:2441/1293p84sf58s482v2dpn0gsd67 is not listed on IDEAS
    10. Alfred Galichon & Marc Henry, 2012. "Dual theory of choice under multivariate risks," SciencePo Working papers Main hal-01024582, HAL.
    11. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-offs: Revealed Preferences over Competiting Characteristics," Working Papers hal-00473173, HAL.
    12. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    13. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
    14. repec:hal:wpspec:info:hdl:2441/7o52iohb7k6srk09mj4j5amb8 is not listed on IDEAS
    15. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    16. Rüschendorf, L. & Rachev, S. T., 1990. "A characterization of random variables with minimum L2-distance," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 48-54, January.
    17. repec:hal:spmain:info:hdl:2441/7o52iohb7k6srk09mj4j5amb8 is not listed on IDEAS
    18. Yannick Malevergne & Didier Sornette, 2006. "Extreme Financial Risks : From Dependence to Risk Management," Post-Print hal-02298069, HAL.
    19. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b1h6b4 is not listed on IDEAS
    20. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc0p30p95 is not listed on IDEAS
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