Convex risk measures on Orlicz spaces: Inf-convolution and shortfall

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11 Citations (Scopus)


We focus on, throughout this paper, convex risk measures defined on Orlicz spaces. In particular, we investigate basic properties of inf-convolutions defined between a convex risk measure and a convex set, and between two convex risk measures. Moreover, we study shortfall risk measures, which are convex risk measures induced by the shortfall risk. By using results on inf-convolutions, we obtain a robust representation result for shortfall risk measures defined on Orlicz spaces under the assumption that the set of hedging strategies has the sequential compactness in a weak sense. We discuss in addition a construction of an example having the sequential compactness.

Original languageEnglish
Pages (from-to)73-88
Number of pages16
JournalMathematics and Financial Economics
Issue number2
Publication statusPublished - 2010 Jul


  • Convex risk measure
  • Inf-convolution
  • Orlicz space
  • Shortfall

ASJC Scopus subject areas

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty


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