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On Kusuoka representation of law invariant risk measures

Alexander Shapiro (ashapiro***at***isye.gatech.edu)

Abstract: In this paper we discuss representations of law invariant coherent risk measures in a form of integrals of the Average Value-at-Risk measures. We show that such integral representation exists iff the dual set of the considered risk measure is generated by one of its elements, and this representation is uniquely defined. On the other hand, representation of risk measures as maximum of such integral forms is not unique.

Keywords: Coherent risk measures, law invariance, Average Value-at-Risk, Fenchel-Moreau Theorem, comonotonic risk measures

Category 1: Stochastic Programming

Category 2: Applications -- OR and Management Sciences (Finance and Economics )

Citation: preprint

Download: [PDF]

Entry Submitted: 09/15/2011
Entry Accepted: 09/15/2011
Entry Last Modified: 05/14/2012

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