2010/10/19 by Ivar Ekeland, Alfred Galichon, Marc Henry
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Algorithm #Applied mathematics #Axiom #Axiomatic system #Characterization (materials science) #Coherence (philosophical gambling strategy) #Computation #Computer science #Discrete mathematics #Econometrics #Economics #Extension (predicate logic) #Financial Risk and Volatility Modeling #Financial economics #Interpretation (philosophy) #Market Dynamics and Volatility #Mathematical economics #Mathematics #Multivariate statistics #Property (philosophy) #Quantile #Risk and Portfolio Optimization #Risk measure #Statistics #Subadditivity #econ.TH
paper · pdf · doi:10.1111/j.1467-9965.2010.00453.x
published as Mathematical Finance 22-1 (2012) pp.109-132 · 33 pages, 6 figures
openalex publication_date 2010/10/19 · arxiv created 2021/02/08 · arxiv updated 2021/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We 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 invariance, subadditivity, and comonotonicity axioms by an equivalent property we call strong coherence and that we argue has more natural economic interpretation. Finally, we reformulate the computation of regular and coherent risk measures as an optimal transportation problem, for which we provide an algorithm and implementation.