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Policy gradient learning methods for stochastic control with exit time and applications to share repurchase pricing

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  • Mohamed Hamdouche
  • Pierre Henry-Labordere
  • Huyen Pham

Abstract

We develop policy gradients methods for stochastic control with exit time in a model-free setting. We propose two types of algorithms for learning either directly the optimal policy or by learning alternately the value function (critic) and the optimal control (actor). The use of randomized policies is crucial for overcoming notably the issue related to the exit time in the gradient computation. We demonstrate the effectiveness of our approach by implementing our numerical schemes in the application to the problem of share repurchase pricing. Our results show that the proposed policy gradient methods outperform PDE or other neural networks techniques in a model-based setting. Furthermore, our algorithms are flexible enough to incorporate realistic market conditions like e.g. price impact or transaction costs.

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  • Mohamed Hamdouche & Pierre Henry-Labordere & Huyen Pham, 2023. "Policy gradient learning methods for stochastic control with exit time and applications to share repurchase pricing," Papers 2302.07320, arXiv.org.
    • Handle: RePEc:arx:papers:2302.07320
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    References listed on IDEAS

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    1. Olivier Guéant & Jiang Pu & Guillaume Royer, 2015. "Accelerated Share Repurchase: Pricing And Execution Strategy," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-31.
    2. Maximilien Germain & Huyên Pham & Xavier Warin, 2021. "Neural networks-based algorithms for stochastic control and PDEs in finance ," Working Papers hal-03115503, HAL.
    3. Olivier Guéant & Iuliia Manziuk & Jiang Pu, 2020. "Accelerated share repurchase and other buyback programs: what neural networks can bring," Quantitative Finance, Taylor & Francis Journals, vol. 20(8), pages 1389-1404, August.
    4. Maximilien Germain & Huyên Pham & Xavier Warin, 2021. "Neural networks-based algorithms for stochastic control and PDEs in finance ," Post-Print hal-03115503, HAL.
    5. S. Jaimungal & D. Kinzebulatov & D. H. Rubisov, 2017. "Optimal accelerated share repurchases," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(3), pages 216-245, May.
    6. Maximilien Germain & Huy^en Pham & Xavier Warin, 2021. "Neural networks-based algorithms for stochastic control and PDEs in finance," Papers 2101.08068, arXiv.org, revised Apr 2021.
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