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A Weak Martingale Approach to Linear-Quadratic McKean-Vlasov Stochastic Control Problems

Author

Listed:
  • Matteo Basei

    (UC Berkeley - University of California [Berkeley] - UC - University of California)

  • Huyên Pham

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique)

Abstract

We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon pro\-blems, and allow notably some coefficients to be stochastic. Extension to the common noise case is also addressed. Our method is based on a suitable version of the martingale formulation for verification theorems in control theory. The optimal control involves the solution to a system of Riccati ordinary differential equations and to a linear mean-field backward stochastic differential equation; existence and uniqueness conditions are provided for such a system. Finally, we illustrate our results through an application to the production of an exhaustible resource. MSC Classification: 49N10, 49L20, 93E20.

Suggested Citation

  • Matteo Basei & Huyên Pham, 2018. "A Weak Martingale Approach to Linear-Quadratic McKean-Vlasov Stochastic Control Problems," Working Papers hal-01648491, HAL.
    • Handle: RePEc:hal:wpaper:hal-01648491
    DOI: 10.1007/s10957-018-01453-z
    Note: View the original document on HAL open archive server: https://hal.science/hal-01648491v2
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    Cited by:

    1. Guanxing Fu & Ulrich Horst, 2018. "Mean-Field Leader-Follower Games with Terminal State Constraint," Papers 1809.04401, arXiv.org.

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