Convex risk measures on Orlicz spaces

Inf-convolution and shortfall

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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
Volume3
Issue number2
DOIs
Publication statusPublished - 2009 Jun

Fingerprint

Inf-convolution
Convex Risk Measures
Orlicz Spaces
Risk Measures
Compactness
Hedging
Convex Sets
Convex risk measures
Convolution
Shortfall risk

Keywords

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

ASJC Scopus subject areas

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

Cite this

Convex risk measures on Orlicz spaces : Inf-convolution and shortfall. / Arai, Takuji.

In: Mathematics and Financial Economics, Vol. 3, No. 2, 06.2009, p. 73-88.

Research output: Contribution to journalArticle

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