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Tail Conditional Expectation for vector-valued Risks

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  • Imen Bentahar
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    Abstract

    In his paper we introduce a quantile-based risk measure for multivariate financial positions "the vector-valued Tail-conditional-expectation (TCE)". We adopt the framework proposed by Jouini, Meddeb, and Touzi [9] to deal with multi-assets portfolios when one accounts for frictions in the financial market. In this framework, the space of risks formed by essentially bounded random vectors, is endowed with some partial vector preorder >= accounting for market frictions. In a first step we provide a definition for quantiles of vector-valued risks which is compatible with the preorder >=. The TCE is then introduced as a natural extension of the "classical" real-valued tail-conditional-expectation. Our main result states that for continuous distributions TCE is equal to a coherent vector-valued risk measure. We also provide a numerical algorithm for computing vector-valued quantiles and TCE.

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-029.pdf
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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-029.

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    Length: 34 pages
    Date of creation: Apr 2006
    Date of revision:
    Handle: RePEc:hum:wpaper:sfb649dp2006-029

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    Related research

    Keywords: Risk measures; vector-valued risk measures; coherent risk-measures; quantiles; tail-conditional-expectation;

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    References

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    1. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
    2. Elyès Jouini & Moncef Meddeb & Nizar Touzi, 2004. "Vector-valued Coherent Risk Measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00167154, HAL.
    3. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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    Cited by:
    1. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
    2. Areski Cousin & Elena Di Bernadino, 2011. "On Multivariate Extensions of Value-at-Risk," Papers 1111.1349, arXiv.org, revised Apr 2013.
    3. Zachary Feinstein & Birgit Rudloff, 2013. "A comparison of techniques for dynamic multivariate risk measures," Papers 1305.2151, arXiv.org, revised Oct 2013.

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