Mathematics and Financial Economics

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

Representation results for law invariant time consistent functions

  • Michael Kupper
  • Walter Schachermayer


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.


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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