= 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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Tail Conditional Expectation for vector-valued Risks

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Imen Bentahar
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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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
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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

Find related papers by JEL classification:
C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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  1. H. Föllmer & A. Schied, . "Convex measures of risk and trading constraints," Sonderforschungsbereich 373 2001-71, Humboldt Universitaet Berlin.
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  2. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July. [Downloadable!] (restricted)
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