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Optimal Control of Diffusion Processes with Terminal Constraint in Law

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  • Samuel Daudin

    (PSL Research University, Université Paris-Dauphine)

Abstract

Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a forward Fokker–Planck equation and a backward Hamilton–Jacobi–Bellman equation are proved using convex duality techniques.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:1:d:10.1007_s10957-022-02053-8
    DOI: 10.1007/s10957-022-02053-8
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    References listed on IDEAS

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    1. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    2. 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.
    3. Ivan Guo & Nicolas Langrené & Grégoire Loeper & Wei Ning, 2022. "Portfolio optimization with a prescribed terminal wealth distribution," Quantitative Finance, Taylor & Francis Journals, vol. 22(2), pages 333-347, February.
    4. Lacker, Daniel, 2015. "Mean field games via controlled martingale problems: Existence of Markovian equilibria," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2856-2894.
    5. Ivan Guo & Grégoire Loeper & Shiyi Wang, 2022. "Calibration of local‐stochastic volatility models by optimal transport," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 46-77, January.
    6. Yuk-Loong Chow & Xiang Yu & Chao Zhou, 2020. "On Dynamic Programming Principle for Stochastic Control Under Expectation Constraints," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 803-818, June.
    7. repec:dau:papers:123456789/3504 is not listed on IDEAS
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