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

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.
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https://hal.archives-ouvertes.fr/hal-01648491
Contributeur : Huyen Pham <>
Soumis le : lundi 22 octobre 2018 - 22:10:44
Dernière modification le : vendredi 16 novembre 2018 - 02:20:25

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  • HAL Id : hal-01648491, version 2
  • ARXIV : 1810.10532

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Matteo Basei, Huyên Pham. A Weak Martingale Approach to Linear-Quadratic McKean-Vlasov Stochastic Control Problems. 2018. 〈hal-01648491v2〉

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