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Discrete-Time Mean-Field Stochastic Control with Partial Observations

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Abstract

We study the optimal control of discrete time mean filed dynamical systems under partial observations. We express the global law of the filtered process as a controlled system with its own dynamics. Following a dynamic programming approach, we prove a verification result providing a solution to the optimal control of the filtered system. As an application, we consider a general linear quadratic example for which an explicit solution is given. We also describe an algorithm for the numerical approximation of the optimal value and provide numerical experiments on a financial example.

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Funding

The second author gratefully acknowledge financial support from the Agence Nationale de la Recherche (ReLISCoP Grant ANR-21-CE40-0001).

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Authors and Affiliations

  1. LPSM, UMR CNRS 8001, Sorbonne University and Université Paris Cité, Paris, France

    Jeremy Chichportich & Idris Kharroubi

  2. Bramham Gardens, Paris, France

    Jeremy Chichportich

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  1. Jeremy Chichportich
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  2. Idris Kharroubi
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Correspondence to Idris Kharroubi.

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Chichportich, J., Kharroubi, I. Discrete-Time Mean-Field Stochastic Control with Partial Observations. Appl Math Optim 88, 90 (2023). https://doi.org/10.1007/s00245-023-10068-4

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  • DOI: https://doi.org/10.1007/s00245-023-10068-4

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