Tail Conditional Expectation for vector-valued Risks
AbstractIn 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.
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Bibliographic InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-029.
Length: 34 pages
Date of creation: Apr 2006
Date of revision:
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; Programming Models; Mathematical and Simulation Modeling - - - General
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-10-07 (All new papers)
- NEP-FIN-2006-10-07 (Finance)
- NEP-FMK-2006-10-07 (Financial Markets)
- NEP-MAC-2006-10-07 (Macroeconomics)
- NEP-RMG-2006-10-07 (Risk Management)
- NEP-UPT-2006-10-07 (Utility Models & Prospect Theory)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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- repec:hal:cesptp:halshs-00167154 is not listed on IDEAS
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"Vector-valued coherent risk measures,"
Finance and Stochastics,
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