Adv. Math. Econ. 15, 27–39 (2011)

A note on robust representations of law-invariant quasiconvex functions

Samuel Drapeau, Michael Kupper^{1} and Ranja Reda ^{3}^{2}

1 Humboldt University Berlin, Unter den Linden 6, 10099 Berlin, Germany (e-mail: drapeau@mathematik.hu-berlin.de, kupper@mathematik.hu-berlin.de)

2 Vienna University of Technology, Wiedner Haupstrasse 8/105-1, 1040 Vienna, Austria (e-mail: ranja.reda@fam.tuwien.ac.at)

Received: June 2, 2010 Revised: October 7, 2010

JEL classification: C02, D80

Mathematical Subject Classification (2010): 91B02, 91B06, 91B30

Abstract. We give robust representations of law-invariant monotone quasiconvex functions. The results are based on Jouini et al. (Adv Math Econ 9:49–71, 2006) and Svindland (Math Financ Econ, 2010), showing that law-invariant quasiconvex functions have the Fatou property.

Key words: Fatou property, law-invariance, risk measure, robust representation

3Financial support from the DFG IRTG 1339 and the Berlin Mathematical School is gratefully acknowledged by Samuel Drapeau. Financial support from MATHEON project E.11 is gratefully acknowledged by both Samuel Drapeau and Michael Kupper. Financial support by the Christian Doppler Research Association (CDG) is gratefully acknowledged by Ranja Reda. The author would like to thank Christina Ziehaus for helpful comments and fruitful discussions.