Tail Conditional Expectation for vector-valued Risks
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  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.
|Date of creation:||Apr 2006|
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- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Cheridito, Patrick & Delbaen, Freddy & Kupper, Michael, 2004. "Coherent and convex monetary risk measures for bounded càdlàg processes," Stochastic Processes and their Applications, Elsevier, vol. 112(1), pages 1-22, July.
- Carlo Acerbi & Dirk Tasche, 2001.
"On the coherence of Expected Shortfall,"
cond-mat/0104295, arXiv.org, revised May 2002.
- Stefan Jaschke & Uwe Küchler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, vol. 5(2), pages 181-200.
- Elyès Jouini & Moncef Meddeb & Nizar Touzi, 2004.
"Vector-valued Coherent Risk Measures,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
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