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The value of shape constraints in discrete moment problems: a review and extension

Author

Listed:
  • Talal Alharbi

    (Qassim University
    Florida Institute of Technology)

  • Anh Ninh

    (William & Mary)

  • Ersoy Subasi

    (Florida Institute of Technology)

  • Munevver Mine Subasi

    (Florida Institute of Technology)

Abstract

This research reviews the use of shape constraints in discrete moment problems. In particular, we investigate the impact of incorporating logconcavity as the new shape constraint in two settings including bounding the k-out-of-n type probabilities and expectations of higher order convex functions of discrete random variables with non-negative and finite support. The bounds are obtained as the optimum values of non-convex nonlinear optimization problem that can be reformulated as a bilinear optimization problem. Numerical experiments show significant improvement in the tightness of the bounds when the shape of underlying unknown probability distribution is prescribed into moment bounding problems. Shape constraints also add values to calculation of the expected stop-loss of aggregated insurance claims within a fixed period. Our finding is expected to expand the scope of applications for both discrete moment problems and logconcavity.

Suggested Citation

  • Talal Alharbi & Anh Ninh & Ersoy Subasi & Munevver Mine Subasi, 2022. "The value of shape constraints in discrete moment problems: a review and extension," Annals of Operations Research, Springer, vol. 318(1), pages 1-31, November.
    • Handle: RePEc:spr:annopr:v:318:y:2022:i:1:d:10.1007_s10479-022-04789-y
    DOI: 10.1007/s10479-022-04789-y
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    References listed on IDEAS

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    1. Anh Ninh & Honggang Hu & David Allen, 2019. "Robust newsvendor problems: effect of discrete demands," Annals of Operations Research, Springer, vol. 275(2), pages 607-621, April.
    2. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.
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    5. Cindy Courtois & Michel Denuit, 2009. "Moment Bounds on Discrete Expected Stop-Loss Transforms, with Applications," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 307-338, September.
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    8. Endre Boros & András Prékopa, 1989. "Closed Form Two-Sided Bounds for Probabilities that At Least r and Exactly r Out of n Events Occur," Mathematics of Operations Research, INFORMS, vol. 14(2), pages 317-342, May.
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