Mathematics and Financial Economics

, Volume 2, Issue 3, pp 189–210 | Cite as

Representation results for law invariant time consistent functions

Article

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 \({c(X)=u^{-1} \circ\mathbb {E}[u(X)]}\) , where \({u:(a, b) \to {\mathbb R}}\) is a strictly increasing, continuous function. The proofs rely on a discrete version of the Skorohod embedding theorem.

Keywords

Law invariance Time consistency Certainty equivalent Dynamic risk measures Skorohod embedding theorem 

Mathematics Subject Classification (2000)

91B30 91B16 91B55 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Vienna Institute of FinanceUniversity of Vienna and Vienna University of Economics and Business AdministrationViennaAustria
  2. 2.University ViennaViennaAustria

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