Robust Arbitrage Conditions for Financial Markets

Derek Singh, Shuzhong Zhang

Research output: Contribution to journalArticlepeer-review


This paper investigated arbitrage properties of financial markets under distributional uncertainty using Wasserstein distance as the ambiguity measure. The weak and strong forms of the classical arbitrage conditions are considered. A relaxation is introduced for which we coin the term statistical arbitrage. The simpler dual formulations of the robust arbitrage conditions are derived. A number of interesting questions arise in this context. One question is: can we compute a critical Wasserstein radius beyond which an arbitrage opportunity exists? What is the shape of the curve mapping the degree of ambiguity to statistical arbitrage levels? Other questions arise regarding the structure of best (worst) case distributions and optimal portfolios. Toward answering these questions, some theory is developed and computational experiments are conducted for specific problem instances. Finally, some open questions and suggestions for future research are discussed.

Original languageEnglish (US)
Article number34
JournalOperations Research Forum
Issue number3
StatePublished - Sep 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.


  • Abitrage
  • Farkas lemma
  • Lagrangian duality
  • Robust optimization
  • Statistical arbitrage
  • Wasserstein distance


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