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Estimation and asymptotics for buffered probability of exceedance

Author

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  • Mafusalov, Alexander
  • Shapiro, Alexander
  • Uryasev, Stan

Abstract

This paper studies statistical properties of empirical (sample) estimates of the buffered probability of exceedance (bPOE). The estimation procedure is based on one dimensional minimization representation of the bPOE. Convergence rates and asymptotic properties of the suggested estimation procedures are investigated. Theoretical predictions are validated with numerical experiments, including a special case of exponential distribution, and a study proposing bPOE modification of minimum volume ellipsoid problem.

Suggested Citation

  • Mafusalov, Alexander & Shapiro, Alexander & Uryasev, Stan, 2018. "Estimation and asymptotics for buffered probability of exceedance," European Journal of Operational Research, Elsevier, vol. 270(3), pages 826-836.
    • Handle: RePEc:eee:ejores:v:270:y:2018:i:3:p:826-836
    DOI: 10.1016/j.ejor.2018.01.021
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    Citations

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    Cited by:

    1. Yongqiao Wang & He Ni & Stan Uryasev, 2023. "Buffered-ranking intervals for virtual profit efficiency analysis," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(4), pages 1149-1181, December.
    2. Pertaia, Giorgi & Prokhorov, Artem & Uryasev, Stan, 2022. "A new approach to credit ratings," Journal of Banking & Finance, Elsevier, vol. 140(C).
    3. Matthew Norton & Valentyn Khokhlov & Stan Uryasev, 2021. "Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation," Annals of Operations Research, Springer, vol. 299(1), pages 1281-1315, April.
    4. Mikhail Zhitlukhin, 2018. "Monotone Sharpe ratios and related measures of investment performance," Papers 1809.10193, arXiv.org, revised May 2021.

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