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Best-Arm Identification Using Extreme Value Theory Estimates of the CVaR

Author

Listed:
  • Dylan Troop

    (Concordia Institute of Information System Engineering, Concordia University, Montréal, QC H3G 1M8, Canada)

  • Frédéric Godin

    (Department of Mathematics and Statistics, Concordia University, Montréal, QC H3G 1M8, Canada)

  • Jia Yuan Yu

    (Concordia Institute of Information System Engineering, Concordia University, Montréal, QC H3G 1M8, Canada)

Abstract

We consider a risk-aware multi-armed bandit framework with the goal of avoiding catastrophic risk. Such a framework has multiple applications in financial risk management. We introduce a new conditional value-at-risk (CVaR) estimation procedure combining extreme value theory with automated threshold selection by ordered goodness-of-fit tests, and we apply this procedure to a pure exploration best-arm identification problem under a fixed budget. We empirically compare our results with the commonly used sample average estimator of the CVaR, and we show a significant performance improvement when the underlying arm distributions are heavy-tailed.

Suggested Citation

  • Dylan Troop & Frédéric Godin & Jia Yuan Yu, 2022. "Best-Arm Identification Using Extreme Value Theory Estimates of the CVaR," JRFM, MDPI, vol. 15(4), pages 1-15, April.
    • Handle: RePEc:gam:jjrfmx:v:15:y:2022:i:4:p:172-:d:789276
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    References listed on IDEAS

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    1. Abdelaati Daouia & Stéphane Girard & Gilles Stupfler, 2018. "Estimation of tail risk based on extreme expectiles," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 263-292, March.
    2. Xiaoguang Huo & Feng Fu, 2017. "Risk-Aware Multi-Armed Bandit Problem with Application to Portfolio Selection," Papers 1709.04415, arXiv.org.
    3. Matthew Norton & Valentyn Khokhlov & Stan Uryasev, 2018. "Calculating CVaR and bPOE for Common Probability Distributions With Application to Portfolio Optimization and Density Estimation," Papers 1811.11301, arXiv.org, revised Feb 2019.
    4. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    5. Max Grazier G'Sell & Stefan Wager & Alexandra Chouldechova & Robert Tibshirani, 2016. "Sequential selection procedures and false discovery rate control," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 423-444, March.
    6. Paul Embrechts & Sidney Resnick & Gennady Samorodnitsky, 1999. "Extreme Value Theory as a Risk Management Tool," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 30-41.
    7. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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    Cited by:

    1. Parisa Davar & Fr'ed'eric Godin & Jose Garrido, 2024. "Catastrophic-risk-aware reinforcement learning with extreme-value-theory-based policy gradients," Papers 2406.15612, arXiv.org, revised Jun 2024.

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