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Robust deep hedging

Author

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  • Eva Lütkebohmert
  • Thorsten Schmidt
  • Julian Sester

Abstract

We study pricing and hedging under parameter uncertainty for a class of Markov processes which we call generalized affine processes and which includes the Black–Scholes model as well as the constant elasticity of variance (CEV) model as special cases. Based on a general dynamic programming principle, we are able to link the associated nonlinear expectation to a variational form of the Kolmogorov equation which opens the door for fast numerical pricing in the robust framework. The main novelty of the paper is that we propose a deep hedging approach which efficiently solves the hedging problem under parameter uncertainty. We numerically evaluate this method on simulated and real data and show that the robust deep hedging outperforms existing hedging approaches in highly volatile periods.

Suggested Citation

  • Eva Lütkebohmert & Thorsten Schmidt & Julian Sester, 2022. "Robust deep hedging," Quantitative Finance, Taylor & Francis Journals, vol. 22(8), pages 1465-1480, August.
    • Handle: RePEc:taf:quantf:v:22:y:2022:i:8:p:1465-1480
    DOI: 10.1080/14697688.2022.2056073
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    • Eva Lutkebohmert & Thorsten Schmidt & Julian Sester, 2021. "Robust deep hedging," Papers 2106.10024, arXiv.org, revised Nov 2021.

    Citations

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    Cited by:

    1. Carl Remlinger & Joseph Mikael & Romuald Elie, 2022. "Robust Operator Learning to Solve PDE," Working Papers hal-03599726, HAL.
    2. Ariel Neufeld & Julian Sester & Mario Šikić, 2023. "Markov decision processes under model uncertainty," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 618-665, July.
    3. Park, Sungwon & Moon, Kyoung-Sook & Kim, Hongjoong, 2025. "Robust deep hedging of equity-linked securities under covariance uncertainty," Finance Research Letters, Elsevier, vol. 85(PE).
    4. François, Pascal & Gauthier, Geneviève & Godin, Frédéric & Mendoza, Carlos Octavio Pérez, 2025. "Is the difference between deep hedging and delta hedging a statistical arbitrage?," Finance Research Letters, Elsevier, vol. 73(C).
    5. Alexandre Carbonneau & Frédéric Godin, 2023. "Deep Equal Risk Pricing of Financial Derivatives with Non-Translation Invariant Risk Measures," Risks, MDPI, vol. 11(8), pages 1-27, August.
    6. Ariel Neufeld & Julian Sester & Daiying Yin, 2022. "Detecting data-driven robust statistical arbitrage strategies with deep neural networks," Papers 2203.03179, arXiv.org, revised Feb 2024.
    7. Alexandre Carbonneau & Fr'ed'eric Godin, 2021. "Deep equal risk pricing of financial derivatives with non-translation invariant risk measures," Papers 2107.11340, arXiv.org.
    8. Lütkebohmert, Eva & Sester, Julian, 2025. "Measuring name concentrations through deep learning," International Review of Financial Analysis, Elsevier, vol. 107(C).

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