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.
Keywords
Cite
@article{arxiv.1810.10532,
title = {A Weak Martingale Approach to Linear-Quadratic McKean-Vlasov Stochastic Control Problems},
author = {Matteo Basei and Huyên Pham},
journal= {arXiv preprint arXiv:1810.10532},
year = {2018}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1711.09390