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Distributionally robust optimization under ambiguity across two layers

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  • Lu, Yingyin
  • Tang, Qihe

Abstract

With general interest in distributionally robust optimization under multilayered ambiguity, we study a stylized model based on the inner product w · X · Y. Here, w is a deterministic, nonnegative d dimensional vector representing a strategy, while X and Y are d dimensional real-valued random vectors representing losses and economic factors, respectively, both subject to ambiguity. We first treat the ambiguity associated with X and Y separately, and then jointly, with each ambiguity set characterized by a Wasserstein ball. In both settings, we derive explicit expressions for the worst-case expectation of w · X · Y. Numerical studies further illustrate how to determine the radii of the Wasserstein balls needed to achieve a prespecified coverage probability.

Suggested Citation

  • Lu, Yingyin & Tang, Qihe, 2026. "Distributionally robust optimization under ambiguity across two layers," Insurance: Mathematics and Economics, Elsevier, vol. 129(C).
    • Handle: RePEc:eee:insuma:v:129:y:2026:i:c:s0167668726000612
    DOI: 10.1016/j.insmatheco.2026.103271
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    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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