On Kusuoka Representation of Law Invariant Risk Measures

  • Authors:

  • Alexander Shapiro

  • Affiliations:

  • School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332

  • Venue:
  • Mathematics of Operations Research
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

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 an 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 a maximum of such integral forms is not unique. The suggested approach gives a constructive way for writing such representations.