Comonotonic measures of multivariates risks
AbstractWe propose a multivariate extension of a well-known characterization by S. Kusuoka of regular and coherent risk measures as maximal correlation functionals. This involves an extension of the notion of comonotonicity to random vectors through generalized quantile functions. Moreover, we propose to replace the current law invari- ance, subadditivity and comonotonicity axioms by an equivalent property we call strong coherence and that we argue has more natural economic interpretation. Finally, we refor- mulate the computation of regular and coherent risk measures as an optimal transportation problem, for which we provide an algorithm and implementation.
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Date of creation: 06 Jul 2009
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regular risk measures; coherent risk measures; comonotonicity; maximal correlation; optimal transportation; strongly coherent risk measures.;
Other versions of this item:
- Ivar Ekeland & Alfred Galichon, 2012. "Comonotonic measures of multivariate risks," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
- Henry, Marc & Galichon, Alfred & Ekeland, Ivar, 2012. "Comonotonic Measures of Multivariate Risks," Economics Papers from University Paris Dauphine 123456789/2278, Paris Dauphine University.
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-07-17 (All new papers)
- NEP-RMG-2009-07-17 (Risk Management)
- NEP-UPT-2009-07-17 (Utility Models & Prospect Theory)
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