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A one-sided Vysochanskii-Petunin inequality with financial applications

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  • Mercadier, Mathieu
  • Strobel, Frank

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

  • Mercadier, Mathieu & Strobel, Frank, 2021. "A one-sided Vysochanskii-Petunin inequality with financial applications," European Journal of Operational Research, Elsevier, vol. 295(1), pages 374-377.
    • Handle: RePEc:eee:ejores:v:295:y:2021:i:1:p:374-377
    DOI: 10.1016/j.ejor.2021.02.041
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    References listed on IDEAS

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    1. Babat, Onur & Vera, Juan C. & Zuluaga, Luis F., 2018. "Computing near-optimal Value-at-Risk portfolios using integer programming techniques," European Journal of Operational Research, Elsevier, vol. 266(1), pages 304-315.
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    5. Mercadier, Mathieu & Lardy, Jean-Pierre, 2019. "Credit spread approximation and improvement using random forest regression," European Journal of Operational Research, Elsevier, vol. 277(1), pages 351-365.
    6. Leung, Melvern & Li, Youwei & Pantelous, Athanasios A. & Vigne, Samuel A., 2021. "Bayesian Value-at-Risk backtesting: The case of annuity pricing," European Journal of Operational Research, Elsevier, vol. 293(2), pages 786-801.
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