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A one-sided Vysochanskii-Petunin inequality with financial applications

Author

Listed:
  • Mathieu Mercadier

    (ESC Clermont-Ferrand - École Supérieure de Commerce (ESC) - Clermont-Ferrand)

  • Frank Strobel

    (University of Birmingham [Birmingham])

Abstract

We derive a one-sided Vysochanskii-Petunin inequality, providing probability bounds for random variables analogous to those given by Cantelli's inequality under the additional assumption of unimodality, potentially relevant for applied statistical practice across a wide range of disciplines. As a possible application of this inequality in a financial context, we examine refined bounds for the individual risk measure of Value-at-Risk, providing a potentially useful alternative benchmark with interesting regulatory implications for the Basel multiplier.

Suggested Citation

  • Mathieu Mercadier & Frank Strobel, 2021. "A one-sided Vysochanskii-Petunin inequality with financial applications," Post-Print hal-03241628, HAL.
    • Handle: RePEc:hal:journl:hal-03241628
    DOI: 10.1016/j.ejor.2021.02.041
    Note: View the original document on HAL open archive server: https://uca.hal.science/hal-03241628v1
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    Cited by:

    1. Carnero, M. Ángeles & León, Ángel & Ñíguez, Trino-Manuel, 2025. "New bounds for tail risk measures," Finance Research Letters, Elsevier, vol. 75(C).
    2. Mercadier, Mathieu & Tarazi, Amine & Armand, Paul & Lardy, Jean-Pierre, 2025. "Monitoring bank risk around the world using unsupervised learning," European Journal of Operational Research, Elsevier, vol. 324(2), pages 590-615.
    3. Mercadier, Mathieu & Strobel, Frank, 2024. "Bank insolvency risk, Z-score measures and unimodal returns: A refinement," The Quarterly Review of Economics and Finance, Elsevier, vol. 98(C).

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