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Deep Bellman Hedging

Author

Listed:
  • Hans Buehler
  • Phillip Murray
  • Ben Wood

Abstract

We present an actor-critic-type reinforcement learning algorithm for solving the problem of hedging a portfolio of financial instruments such as securities and over-the-counter derivatives using purely historic data. The key characteristics of our approach are: the ability to hedge with derivatives such as forwards, swaps, futures, options; incorporation of trading frictions such as trading cost and liquidity constraints; applicability for any reasonable portfolio of financial instruments; realistic, continuous state and action spaces; and formal risk-adjusted return objectives. Most importantly, the trained model provides an optimal hedge for arbitrary initial portfolios and market states without the need for re-training. We also prove existence of finite solutions to our Bellman equation, and show the relation to our vanilla Deep Hedging approach

Suggested Citation

  • Hans Buehler & Phillip Murray & Ben Wood, 2022. "Deep Bellman Hedging," Papers 2207.00932, arXiv.org, revised Jan 2023.
    • Handle: RePEc:arx:papers:2207.00932
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    References listed on IDEAS

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    2. Igor Halperin, 2019. "The QLBS Q-Learner goes NuQLear: fitted Q iteration, inverse RL, and option portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1543-1553, September.
    3. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Aharon Ben‐Tal & Marc Teboulle, 2007. "An Old‐New Concept Of Convex Risk Measures: The Optimized Certainty Equivalent," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 449-476, July.
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