Tight Bounds for a Class of Data-Driven Distributionally Robust Risk Measures

Derek Singh, Shuzhong Zhang

Research output: Contribution to journalArticlepeer-review


This paper expands the notion of robust moment problems to incorporate distributional ambiguity using Wasserstein distance as the ambiguity measure. The classical Chebyshev-Cantelli (zeroth partial moment) inequalities, Scarf and Lo (first partial moment) bounds, and semideviation (second partial moment) in one dimension are investigated. The infinite dimensional primal problems are formulated and the simpler finite dimensional dual problems are derived. A principal motivating question is how does data-driven distributional ambiguity affect the moment bounds. Towards answering this question, some theory is developed and computational experiments are conducted for specific problem instances in inventory control and portfolio management. Finally some open questions and suggestions for future research are discussed.

Original languageEnglish (US)
JournalApplied Mathematics and Optimization
Issue number1
StatePublished - Feb 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Chebyshev-Cantelli inequality
  • Lagrangian duality
  • Partial moments
  • Robust moment problems
  • Scarf and Lo bounds
  • Wasserstein distance


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