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Bounds for functions of multivariate risks

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  • Embrechts, Paul
  • Puccetti, Giovanni
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    Abstract

    Li et al. [Distributions with Fixed Marginals and Related Topics, vol. 28, Institute of Mathematics and Statistics, Hayward, CA, 1996, pp. 198-212] provide bounds on the distribution and on the tail for functions of dependent random vectors having fixed multivariate marginals. In this paper, we correct a result stated in the above article and we give improved bounds in the case of the sum of identically distributed random vectors. Moreover, we provide the dependence structures meeting the bounds when the fixed marginals are uniformly distributed on the k-dimensional hypercube. Finally, a definition of a multivariate risk measure is given along with actuarial/financial applications.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 2 (February)
    Pages: 526-547
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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:2:p:526-547

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    For corrections or technical questions regarding this item, or to correct its listing, contact: (Jeroen Loos).

    Related research

    Keywords: Multivariate marginals Coupling Dual bounds Value-at-Risk Risk measures;

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    Citations

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    Cited by:
    1. Areski Cousin & Elena Di Bernadino, 2011. "A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation," Working Papers hal-00638382, HAL.
    2. Ludger Rüschendorf, 2012. "Worst case portfolio vectors and diversification effects," Finance and Stochastics, Springer, vol. 16(1), pages 155-175, January.
    3. Ignacio Cascos & Ilya Molchanov, 2006. "Multivariate Risks And Depth-Trimmed Regions," Statistics and Econometrics Working Papers ws063815, Universidad Carlos III, Departamento de Estadística y Econometría.
    4. Areski Cousin & Elena Di Bernadino, 2011. "A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation," Quantitative Finance Papers 1111.1349, arXiv.org.

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