Linear-quadratic McKean-Vlasov stochastic control problems with random coefficients on finite and infinite horizon, and applications *
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 problems , and allow notably some coefficients to be stochastic. Our method is based on a suitable extension 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 two applications with explicit solutions: the first one deals with a portfolio liquidation problem with trade crowding, and the second one considers an economic model of substitutable production goods. MSC Classification: 49N10, 49L20, 93E20.
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courbesLQMKVparamNu30.pdf (14.98 Ko)
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courbesLQMKVparamQ30.pdf (33.16 Ko)
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