Schur convex functionals: Fatou property and representation

Bogdan Grechuk, Michael Zabarankin

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

The Fatou property for every Schur convex lower semicontinuous (l.s.c.) functional on a general probability space is established. As a result, the existing quantile representations for Schur convex l.s.c. positively homogeneous convex functionals, established onfor eitherp= 1orp=∞and with the requirement of the Fatou property, are generalized for, with no requirement of the Fatou property. In particular, the existing quantile representations for law invariant coherent risk measures and law invariant deviation measures on an atomless probability space are extended for a general probability space.

Original languageEnglish
Pages (from-to)411-418
Number of pages8
JournalMathematical Finance
Volume22
Issue number2
DOIs
StatePublished - Apr 2012

Keywords

  • Deviation measures
  • Error measures
  • Quantile representation
  • Risk measures
  • Schur convexity

Fingerprint

Dive into the research topics of 'Schur convex functionals: Fatou property and representation'. Together they form a unique fingerprint.

Cite this