Ontology type: schema:ScholarlyArticle Open Access: True
2009-09-01
AUTHORSMichael Kupper, Walter Schachermayer
ABSTRACTWe show that the only dynamic risk measure which is law invariant, time consistent and relevant is the entropic one. Moreover, a real valued function c on L∞(a, b) is normalized, strictly monotone, continuous, law invariant, time consistent and has the Fatou property if and only if it is of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c(X)=u^{-1} \circ\mathbb {E}[u(X)]}$$\end{document} , where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${u:(a, b) \to {\mathbb R}}$$\end{document} is a strictly increasing, continuous function. The proofs rely on a discrete version of the Skorohod embedding theorem. More... »
PAGES189-210
http://scigraph.springernature.com/pub.10.1007/s11579-009-0019-9
DOIhttp://dx.doi.org/10.1007/s11579-009-0019-9
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