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Pré-Publication, Document De Travail Année : 2019

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

Matteo Basei
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Résumé

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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Dates et versions

hal-01648491 , version 1 (26-11-2017)
hal-01648491 , version 2 (22-10-2018)

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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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