Worst-case CVaR based portfolio optimization models with applications to scenario planning

Xiaojiao Tong, Felix Wu, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

21 Citations (Scopus)


This article studies three robust portfolio optimization models under partially known distributions. The proposed models are composed of min-max optimization problems under the worst-case conditional value-at-risk consideration. By using the duality theory, the models are reduced to simple mathematical programming problems where the underlying random variables have a mixture distribution or a box discrete distribution. They become linear programming problems when the loss function is linear. The solutions between the original problems and the reduced ones are proved to be identical. Furthermore, for the mixture distribution, it is shown that the three profit-risk optimization models have the same efficient frontier. The reformulated linear program shows the usability of the method. As an illustration, the robust models are applied to allocations of generation assets in power markets. Numerical simulations confirm the theoretical analysis.
Original languageEnglish
Pages (from-to)933-958
Number of pages26
JournalOptimization Methods and Software
Issue number6
Publication statusPublished - 1 Dec 2009


  • Box discrete distribution
  • Conditional value-at-risk (CVaR)
  • Generation asset
  • Mixture distribution
  • Portfolio optimization
  • Worst-case CVaR (WCVaR)

ASJC Scopus subject areas

  • Control and Optimization
  • Software
  • Applied Mathematics


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