-

 

 

 




Optimization Online





 

Kusuoka Representation of Higher Order Dual Risk Measures

Darinka Dentcheva(darinka.dentcheva***at***stevens.edu)
Spiridon Penev(spiro***at***maths.unsw.edu.au)
Andrzej Ruszczynski(rusz***at***business.rutgers.edu)

Abstract: We derive representations of higher order dual measures of risk in $\mathcal{L}^p$ spaces as suprema of integrals of Average Values at Risk with respect to probability measures on $(0,1]$ (Kusuoka representations). The suprema are taken over convex sets of probability measures. The sets are described by constraints on the dual norms of certain transformations of distribution functions. For $p=2$, we obtain a special description of the set and we relate the measures of risk to the Fano factor in statistics.

Keywords: Lorenz curve, quantile functions, average value at risk, coherent measures of risk, Fano factor, optimization, duality

Category 1: Stochastic Programming

Citation:

Download: [PDF]

Entry Submitted: 03/24/2010
Entry Accepted: 03/25/2010
Entry Last Modified: 03/24/2010

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 Programming Society