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Journal of Industrial and Management Optimization

2026, Volume 22, Issue 8: 4039-4087. doi: 10.3934/jimo.2026143
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Research article

Distributionally robust automation under overdispersed count risk: Ambiguity sets, tail protection, and oracle-relative policy gap

  • 1.
    Department of Computer Science, Gwinnett Technical College, Georgia, USA
  • 2.
    Department of Decision Sciences and Economics, College of Business, Texas A&M University–Corpus Christi, Texas, USA
  • 3.
    Department of Finance and Accounting, East Asia University of Technology, Bac Ninh, Vietnam
  • 4.
    Department of Economics and Business Administration, Nghe An University, Nghe An Province, Vietnam
  • 5.
    School of Economics and International Business, Foreign Trade University, Hanoi, Vietnam
  • Published: 27 July 2026

  • 90C15, 90C17, 90C39, 60E05, 62P20

  • Automation under clustered count risk can be fragile when a fitted model understates dispersion or upper-tail exposure. We developed a distributionally robust sequential automation framework in which a protective intervention is selected based on fitted or ambiguity-adjusted exposure and the previously implemented level. The control may represent hedging, monitoring, preventive maintenance, or automated incident response. Convex implementation and adjustment costs produce history-dependent decisions without a Bellman recursion or specified transition kernel. A local ambiguity set perturbs the fitted negative binomial (NB) mean and dispersion. We established existence and uniqueness, monotonicity, an activation condition, and adjustment-induced policy persistence. Balanced experiments include favorable, neutral, adverse, and reverse misspecification, revealing protection benefits and over-intervention costs of robustness. Using 437 monthly Standard & Poor's 500 (S&P 500) jump counts, the out-of-sample illustration shows a variance-to-mean ratio of 4.811 and that the NB model fits substantially better than the Poisson benchmark. Robust policies reduce tail loss by 1.90%–17.11%; total-cost estimates also improve, although bootstrap intervals include zero. The financial application illustrates the framework, while the theory extends to other clustered count-risk settings.

    Citation: Jinho Cha, Long Pham, Minh Ngo Thi, Ho Thi Hien, Hai Thi Bich Vu. Distributionally robust automation under overdispersed count risk: Ambiguity sets, tail protection, and oracle-relative policy gap[J]. Journal of Industrial and Management Optimization, 2026, 22(8): 4039-4087. doi: 10.3934/jimo.2026143

    Related Papers:

  • Automation under clustered count risk can be fragile when a fitted model understates dispersion or upper-tail exposure. We developed a distributionally robust sequential automation framework in which a protective intervention is selected based on fitted or ambiguity-adjusted exposure and the previously implemented level. The control may represent hedging, monitoring, preventive maintenance, or automated incident response. Convex implementation and adjustment costs produce history-dependent decisions without a Bellman recursion or specified transition kernel. A local ambiguity set perturbs the fitted negative binomial (NB) mean and dispersion. We established existence and uniqueness, monotonicity, an activation condition, and adjustment-induced policy persistence. Balanced experiments include favorable, neutral, adverse, and reverse misspecification, revealing protection benefits and over-intervention costs of robustness. Using 437 monthly Standard & Poor's 500 (S&P 500) jump counts, the out-of-sample illustration shows a variance-to-mean ratio of 4.811 and that the NB model fits substantially better than the Poisson benchmark. Robust policies reduce tail loss by 1.90%–17.11%; total-cost estimates also improve, although bootstrap intervals include zero. The financial application illustrates the framework, while the theory extends to other clustered count-risk settings.



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