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Market making and incentives design in the presence of a dark pool: a deep reinforcement learning approach

Author

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  • Bastien Baldacci
  • Iuliia Manziuk
  • Thibaut Mastrolia
  • Mathieu Rosenbaum

Abstract

We consider the issue of a market maker acting at the same time in the lit and dark pools of an exchange. The exchange wishes to establish a suitable make-take fees policy to attract transactions on its venues. We first solve the stochastic control problem of the market maker without the intervention of the exchange. Then we derive the equations defining the optimal contract to be set between the market maker and the exchange. This contract depends on the trading flows generated by the market maker's activity on the two venues. In both cases, we show existence and uniqueness, in the viscosity sense, of the solutions of the Hamilton-Jacobi-Bellman equations associated to the market maker and exchange's problems. We finally design deep reinforcement learning algorithms enabling us to approximate efficiently the optimal controls of the market maker and the optimal incentives to be provided by the exchange.

Suggested Citation

  • Bastien Baldacci & Iuliia Manziuk & Thibaut Mastrolia & Mathieu Rosenbaum, 2019. "Market making and incentives design in the presence of a dark pool: a deep reinforcement learning approach," Papers 1912.01129, arXiv.org.
    • Handle: RePEc:arx:papers:1912.01129
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    References listed on IDEAS

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    1. Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2018. "Dynamic programming approach to principal–agent problems," Finance and Stochastics, Springer, vol. 22(1), pages 1-37, January.
    2. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Dealing with the Inventory Risk. A solution to the market making problem," Papers 1105.3115, arXiv.org, revised Aug 2012.
    3. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    4. Bastien Baldacci & Dylan Possamai & Mathieu Rosenbaum, 2019. "Optimal make take fees in a multi market maker environment," Papers 1907.11053, arXiv.org, revised Mar 2021.
    5. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
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    Citations

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    Cited by:

    1. Bruno Gav{s}perov & Zvonko Kostanjv{c}ar, 2022. "Deep Reinforcement Learning for Market Making Under a Hawkes Process-Based Limit Order Book Model," Papers 2207.09951, arXiv.org.
    2. Burcu Aydoğan & Ömür Uğur & Ümit Aksoy, 2023. "Optimal Limit Order Book Trading Strategies with Stochastic Volatility in the Underlying Asset," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 289-324, June.
    3. Arthur Charpentier & Romuald Elie & Carl Remlinger, 2020. "Reinforcement Learning in Economics and Finance," Papers 2003.10014, arXiv.org.
    4. Ben Hambly & Renyuan Xu & Huining Yang, 2021. "Recent Advances in Reinforcement Learning in Finance," Papers 2112.04553, arXiv.org, revised Feb 2023.
    5. Bruno Gašperov & Stjepan Begušić & Petra Posedel Šimović & Zvonko Kostanjčar, 2021. "Reinforcement Learning Approaches to Optimal Market Making," Mathematics, MDPI, vol. 9(21), pages 1-22, October.
    6. Ben Hambly & Renyuan Xu & Huining Yang, 2023. "Recent advances in reinforcement learning in finance," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 437-503, July.
    7. Bastien Baldacci & Philippe Bergault, 2021. "Optimal incentives in a limit order book: a SPDE control approach," Papers 2112.00375, arXiv.org, revised Oct 2022.
    8. Bastien Baldacci & Iuliia Manziuk, 2020. "Adaptive trading strategies across liquidity pools," Papers 2008.07807, arXiv.org.
    9. Arthur Charpentier & Romuald Élie & Carl Remlinger, 2023. "Reinforcement Learning in Economics and Finance," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 425-462, June.
    10. Alberto Gennaro & Thibaut Mastrolia, 2024. "Delegated portfolio management with random default," Papers 2410.13103, arXiv.org.

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