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Distributionally Robust Profit Opportunities

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  • Derek Singh
  • Shuzhong Zhang

Abstract

This paper expands the notion of robust profit opportunities in financial markets to incorporate distributional uncertainty using Wasserstein distance as the ambiguity measure. Financial markets with risky and risk-free assets are considered. The infinite dimensional primal problems are formulated, leading to their simpler finite dimensional dual problems. A principal motivating question is how does distributional uncertainty help or hurt the robustness of the profit opportunity. Towards answering this question, some theory is developed and computational experiments are conducted. Finally some open questions and suggestions for future research are discussed.

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  • Derek Singh & Shuzhong Zhang, 2020. "Distributionally Robust Profit Opportunities," Papers 2006.11279, arXiv.org.
    • Handle: RePEc:arx:papers:2006.11279
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    File URL: http://arxiv.org/pdf/2006.11279
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    References listed on IDEAS

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    1. Ostrovski, Vladimir, 2013. "Stability of no-arbitrage property under model uncertainty," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 89-92.
    2. Jos F. Sturm & Shuzhong Zhang, 2003. "On Cones of Nonnegative Quadratic Functions," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 246-267, May.
    3. Li Chen & Simai He & Shuzhong Zhang, 2011. "When all risk-adjusted performance measures are the same: in praise of the Sharpe ratio," Quantitative Finance, Taylor & Francis Journals, vol. 11(10), pages 1439-1447.
    4. Derek Singh & Shuzhong Zhang, 2020. "Robust Arbitrage Conditions for Financial Markets," Papers 2004.09432, arXiv.org.
    5. Jose Blanchet & Karthyek Murthy, 2019. "Quantifying Distributional Model Risk via Optimal Transport," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 565-600, May.
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    Cited by:

    1. Derek Singh & Shuzhong Zhang, 2020. "Tight Bounds for a Class of Data-Driven Distributionally Robust Risk Measures," Papers 2010.05398, arXiv.org, revised Oct 2020.

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