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Deep combinatorial optimisation for optimal stopping time problems : application to swing options pricing

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  • Thomas Deschatre
  • Joseph Mikael

Abstract

A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the derivation of a dynamic programming principle nor a backward stochastic differential equation. Unlike continuous optimization where automatic differentiation is used directly, we propose a likelihood ratio method for gradient computation. Numerical tests are done on the pricing of American and swing options. The proposed algorithm succeeds in pricing high dimensional American and swing options in a reasonable computation time, which is not possible with classical algorithms.

Suggested Citation

  • Thomas Deschatre & Joseph Mikael, 2020. "Deep combinatorial optimisation for optimal stopping time problems : application to swing options pricing," Papers 2001.11247, arXiv.org, revised Jan 2021.
    • Handle: RePEc:arx:papers:2001.11247
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    File URL: http://arxiv.org/pdf/2001.11247
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    References listed on IDEAS

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    1. Alfredo Ibáñez, 2004. "Valuation by Simulation of Contingent Claims with Multiple Early Exercise Opportunities," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 223-248, April.
    2. René Carmona & Nizar Touzi, 2008. "Optimal Multiple Stopping And Valuation Of Swing Options," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 239-268, April.
    3. repec:dau:papers:123456789/4273 is not listed on IDEAS
    4. Christophe Barrera-Esteve & Florent Bergeret & Charles Dossal & Emmanuel Gobet & Asma Meziou & Rémi Munos & Damien Reboul-Salze, 2006. "Numerical Methods for the Pricing of Swing Options: A Stochastic Control Approach," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 517-540, December.
    5. Bouchard, Bruno & Chassagneux, Jean-François, 2008. "Discrete-time approximation for continuously and discretely reflected BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2269-2293, December.
    6. repec:dau:papers:123456789/11531 is not listed on IDEAS
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    Cited by:

    1. Francesco Giuseppe Cordoni & Luca Di Persio & Yilun Jiang, 2020. "A Bank Salvage Model by Impulse Stochastic Controls," Risks, MDPI, vol. 8(2), pages 1-31, June.

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