Robust Arbitrage Tests Under Wasserstein Distributional Uncertainty

Summary

The paper studies whether classical arbitrage conditions continue to hold when the market’s probability distribution is uncertain. It measures that uncertainty with Wasserstein distance and examines both weak and strong versions of the standard arbitrage conditions. The framework also introduces a relaxed condition called statistical arbitrage, intended to characterize opportunities when the usual requirements may not apply exactly.

The authors derive simpler dual formulations and develop theory and computational experiments for selected problem instances. They investigate questions such as how much distributional ambiguity is needed before an arbitrage opportunity appears, how statistical arbitrage changes as ambiguity grows, and what the best- or worst-case distributions and portfolios look like. The available description does not provide specific numerical findings or establish broad empirical performance. Its contribution is primarily a theoretical and computational framework; results may depend on the chosen market model, ambiguity measure, and problem instance.

Key ideas

• The paper analyzes weak and strong arbitrage conditions when the underlying probability distribution is uncertain.
• Wasserstein distance serves as the measure of distributional ambiguity.
• A relaxed condition, termed statistical arbitrage, extends the analysis beyond classical arbitrage requirements.
• Dual formulations are derived to simplify the robust arbitrage conditions.
• The work explores ambiguity thresholds, statistical arbitrage levels, and optimal portfolios through theory and computational examples.

Tags

# Robust Arbitrage Conditions for Financial Markets


# Robust Arbitrage Conditions for Financial Markets









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.

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