Schur Convex Functionals: Fatou Property and Representation

8 Pages Posted: 11 Feb 2012

See all articles by Bogdan Grechuk

Bogdan Grechuk

affiliation not provided to SSRN

Michael Zabarankin

Stevens Institute of Technology - Department of Mathematical Sciences

Date Written: April 2012

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 on for either or 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.

Keywords: Schur convexity, risk measures, quantile representation, deviation measures, error measures

Suggested Citation

Grechuk, Bogdan and Zabarankin, Michael, Schur Convex Functionals: Fatou Property and Representation (April 2012). Mathematical Finance, Vol. 22, Issue 2, pp. 411-418, 2012, Available at SSRN: https://ssrn.com/abstract=2003206 or http://dx.doi.org/10.1111/j.1467-9965.2010.00464.x

Bogdan Grechuk (Contact Author)

affiliation not provided to SSRN

No Address Available

Michael Zabarankin

Stevens Institute of Technology - Department of Mathematical Sciences ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://personal.stevens.edu/~mzabaran/

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