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Catastrophic-risk-aware reinforcement learning with extreme-value-theory-based policy gradients

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  • Parisa Davar
  • Fr'ed'eric Godin
  • Jose Garrido

Abstract

This paper tackles the problem of mitigating catastrophic risk (which is risk with very low frequency but very high severity) in the context of a sequential decision making process. This problem is particularly challenging due to the scarcity of observations in the far tail of the distribution of cumulative costs (negative rewards). A policy gradient algorithm is developed, that we call POTPG. It is based on approximations of the tail risk derived from extreme value theory. Numerical experiments highlight the out-performance of our method over common benchmarks, relying on the empirical distribution. An application to financial risk management, more precisely to the dynamic hedging of a financial option, is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2406.15612
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    References listed on IDEAS

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    1. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    2. Saeed Marzban & Erick Delage & Jonathan Yu-Meng Li, 2023. "Deep reinforcement learning for option pricing and hedging under dynamic expectile risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 23(10), pages 1411-1430, October.
    3. Alexandre Carbonneau & Fr'ed'eric Godin, 2021. "Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments," Papers 2102.12694, arXiv.org.
    4. Alexandre Carbonneau & Frédéric Godin, 2021. "Equal risk pricing of derivatives with deep hedging," Quantitative Finance, Taylor & Francis Journals, vol. 21(4), pages 593-608, April.
    5. Anthony Coache & Sebastian Jaimungal & 'Alvaro Cartea, 2022. "Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning," Papers 2206.14666, arXiv.org, revised May 2023.
    6. David Wu & Sebastian Jaimungal, 2023. "Robust Risk-Aware Option Hedging," Papers 2303.15216, arXiv.org, revised Dec 2023.
    7. Frédéric Godin & Silvia Mayoral & Manuel Morales, 2012. "Contingent Claim Pricing Using a Normal Inverse Gaussian Probability Distortion Operator," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(3), pages 841-866, September.
    8. David Wu & Sebastian Jaimungal, 2023. "Robust Risk-Aware Option Hedging," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(3), pages 153-174, May.
    9. F. Godin, 2016. "Minimizing CVaR in global dynamic hedging with transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 461-475, March.
    10. 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.
    11. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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