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Robust Wasserstein Optimization and its Application in Mean-CVaR

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  • Xin Hai
  • Kihun Nam

Abstract

We refer to recent inference methodology and formulate a framework for solving the distributionally robust optimization problem, where the true probability measure is inside a Wasserstein ball around the empirical measure and the radius of the Wasserstein ball is determined by the empirical data. We transform the robust optimization into a non-robust optimization with a penalty term and provide the selection of the Wasserstein ambiguity set's size. Moreover, we apply this framework to the robust mean-CVaR optimization problem and the numerical experiments of the US stock market show impressive results compared to other popular strategies.

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  • Xin Hai & Kihun Nam, 2023. "Robust Wasserstein Optimization and its Application in Mean-CVaR," Papers 2306.15524, arXiv.org.
    • Handle: RePEc:arx:papers:2306.15524
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    References listed on IDEAS

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    1. R.H. Tütüncü & M. Koenig, 2004. "Robust Asset Allocation," Annals of Operations Research, Springer, vol. 132(1), pages 157-187, November.
    2. Zhilin Kang & Xun Li & Zhongfei Li & Shushang Zhu, 2019. "Data-driven robust mean-CVaR portfolio selection under distribution ambiguity," Quantitative Finance, Taylor & Francis Journals, vol. 19(1), pages 105-121, January.
    3. Shushang Zhu & Masao Fukushima, 2009. "Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management," Operations Research, INFORMS, vol. 57(5), pages 1155-1168, October.
    4. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    5. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    6. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    7. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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