Annals of Operations Research

, Volume 152, Issue 1, pp 227–256 | Cite as

Conditional value at risk and related linear programming models for portfolio optimization

  • Renata Mansini
  • Włodzimierz OgryczakEmail author
  • M. Grazia Speranza


Many risk measures have been recently introduced which (for discrete random variables) result in Linear Programs (LP). While some LP computable risk measures may be viewed as approximations to the variance (e.g., the mean absolute deviation or the Gini’s mean absolute difference), shortfall or quantile risk measures are recently gaining more popularity in various financial applications. In this paper we study LP solvable portfolio optimization models based on extensions of the Conditional Value at Risk (CVaR) measure. The models use multiple CVaR measures thus allowing for more detailed risk aversion modeling. We study both the theoretical properties of the models and their performance on real-life data.


Portfolio optimization Mean-risk models Linear programming Stochastic dominance Conditional Value at Risk Gini’s mean difference 


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Renata Mansini
    • 1
  • Włodzimierz Ogryczak
    • 2
    Email author
  • M. Grazia Speranza
    • 1
  1. 1.Department of Electronics for AutomationUniversity of BresciaBresciaItaly
  2. 2.Institute of Control and Computation EngineeringWarsaw University of TechnologyWarsawPoland

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