  This paper investigates 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. Towards 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.
