-

 

 

 




Optimization Online





 

Kusuoka Representations of Coherent Risk Measures in General Probability Spaces

Nilay Noyan(nnoyan***at***sabanciuniv.edu)
Gabor Rudolf(grudolf***at***sabanciuniv.edu)

Abstract: Kusuoka representations provide an important and useful characterization of law invariant coherent risk measures in atomless probability spaces. However, the applicability of these results is limited by the fact that such representations do not always exist in probability spaces with atoms, such as finite probability spaces. We introduce the class of functionally coherent risk measures, which allow us to use Kusuoka representations in any probability space. We show that this class contains every law invariant risk measure that can be coherently extended to a family containing all finite discrete distributions. Thus, it is possible to preserve the desirable properties of law invariant coherent risk measures on atomless spaces without sacrificing generality. We also specialize our results to risk measures on finite probability spaces, and prove a denseness result about the family of risk measures with finite Kusuoka representations.

Keywords: Kusuoka representation; coherent risk measures; spectral risk measures; law invariance; comonotonicity

Category 1: Stochastic Programming

Citation:

Download: [PDF]

Entry Submitted: 05/03/2013
Entry Accepted: 05/03/2013
Entry Last Modified: 05/03/2013

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society