Representation results for law invariant time consistent functions View Full Text


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Article Info

DATE

2009-09-01

AUTHORS

Michael Kupper, Walter Schachermayer

ABSTRACT

We 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... »

PAGES

189-210

References to SciGraph publications

  • 2006-11-04. A super-replication theorem in Kabanov’s model of transaction costs in FINANCE AND STOCHASTICS
  • 2008-07-29. Dual characterization of properties of risk measures on Orlicz hearts in MATHEMATICS AND FINANCIAL ECONOMICS
  • 2001. On law invariant coherent risk measures in ADVANCES IN MATHEMATICAL ECONOMICS
  • 2006. Law invariant risk measures have the Fatou property in ADVANCES IN MATHEMATICAL ECONOMICS
  • 2009-12-09. Representation of the penalty term of dynamic concave utilities in FINANCE AND STOCHASTICS
  • 2005. Law invariant convex risk measures in ADVANCES IN MATHEMATICAL ECONOMICS
  • 2006. The Structure of m–Stable Sets and in Particular of the Set of Risk Neutral Measures in IN MEMORIAM PAUL-ANDRÉ MEYER
  • 2003. Handbook of Means and Their Inequalities in NONE
  • 2002. Coherent Risk Measures on General Probability Spaces in ADVANCES IN FINANCE AND STOCHASTICS
  • 2006-11-14. Coherent multiperiod risk adjusted values and Bellman’s principle in ANNALS OF OPERATIONS RESEARCH
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11579-009-0019-9

    DOI

    http://dx.doi.org/10.1007/s11579-009-0019-9

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1021648094


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