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Duality theorem for the stochastic optimal control problem

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  • Mikami, Toshio
  • Thieullen, Michèle

Abstract

We prove a duality theorem for the stochastic optimal control problem with a convex cost function and show that the minimizer satisfies a class of forward-backward stochastic differential equations. As an application, we give an approach, from the duality theorem, to h-path processes for diffusion processes.

Suggested Citation

  • Mikami, Toshio & Thieullen, Michèle, 2006. "Duality theorem for the stochastic optimal control problem," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1815-1835, December.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:12:p:1815-1835
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    References listed on IDEAS

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    1. Rüschendorf, L. & Thomsen, W., 1993. "Note on the Schrödinger equation and I-projections," Statistics & Probability Letters, Elsevier, vol. 17(5), pages 369-375, August.
    2. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
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    Cited by:

    1. Samuel Daudin, 2022. "Optimal Control of Diffusion Processes with Terminal Constraint in Law," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 1-41, October.
    2. Lassalle, Rémi & Cruzeiro, Ana Bela, 2019. "An intrinsic calculus of variations for functionals of laws of semi-martingales," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3585-3618.
    3. Ivan Guo & Gregoire Loeper, 2018. "Path Dependent Optimal Transport and Model Calibration on Exotic Derivatives," Papers 1812.03526, arXiv.org, revised Sep 2020.
    4. Montacer Essid & Michele Pavon, 2019. "Traversing the Schrödinger Bridge Strait: Robert Fortet’s Marvelous Proof Redux," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 23-60, April.
    5. Yongxin Chen & Tryphon T. Georgiou & Michele Pavon, 2016. "On the Relation Between Optimal Transport and Schrödinger Bridges: A Stochastic Control Viewpoint," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 671-691, May.
    6. Luo, Peng & Menoukeu-Pamen, Olivier & Tangpi, Ludovic, 2022. "Strong solutions of forward–backward stochastic differential equations with measurable coefficients," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 1-22.
    7. Toshio Mikami, 2021. "Stochastic optimal transport revisited," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-26, February.

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