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

Matteo Basei () and Huyên Pham ()
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Matteo Basei: University of California, Berkeley
Huyên Pham: Université Paris Diderot and CREST-ENSAE

Journal of Optimization Theory and Applications, 2019, vol. 181, issue 2, No 1, 347-382

Abstract: Abstract We propose a simple and direct approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon problems 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.

Keywords: Mean-field SDEs; Linear-quadratic optimal control; Weak martingale optimality principle; Riccati equation; 49N10; 49L20; 93E20 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-018-01453-z

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