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Dynamic programming principle and computable prices in financial market models with transaction costs

Author

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  • Emmanuel Lépinette

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Duc Thinh Vu

Abstract

How to compute (super) hedging costs in rather general financial market models with transaction costs in discrete-time ? Despite the huge literature on this topic, most of results are characterizations of the super-hedging prices while it remains difficult to deduce numerical procedure to estimate them. We establish here a dynamic programming principle and we prove that it is possible to implement it under some conditions on the conditional supports of the price and volume processes for a large class of market models including convex costs such as order books but also non convex costs, e.g. fixed cost models.

Suggested Citation

  • Emmanuel Lépinette & Duc Thinh Vu, 2023. "Dynamic programming principle and computable prices in financial market models with transaction costs," Post-Print hal-03284655, HAL.
    • Handle: RePEc:hal:journl:hal-03284655
    DOI: 10.1016/j.jmaa.2023.127068
    Note: View the original document on HAL open archive server: https://hal.science/hal-03284655
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    References listed on IDEAS

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    2. Emmanuel Denis & Yuri Kabanov, 2010. "Mean square error for the Leland–Lott hedging strategy: convex pay-offs," Finance and Stochastics, Springer, vol. 14(4), pages 625-667, December.
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    5. Meriam El Mansour & Emmanuel Lépinette, 2020. "Conditional Interior and Conditional Closure of Random Sets," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 356-369, November.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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