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September 2015 Forward–backward stochastic differential equations and controlled McKean–Vlasov dynamics
René Carmona, François Delarue
Ann. Probab. 43(5): 2647-2700 (September 2015). DOI: 10.1214/14-AOP946

Abstract

The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of McKean–Vlasov type. Motivated by the recent interest in mean-field games, we highlight the connection and the differences between the two sets of problems. We prove a new version of the stochastic maximum principle and give sufficient conditions for existence of an optimal control. We also provide examples for which our sufficient conditions for existence of an optimal solution are satisfied. Finally we show that our solution to the control problem provides approximate equilibria for large stochastic controlled systems with mean-field interactions when subject to a common policy.

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René Carmona. François Delarue. "Forward–backward stochastic differential equations and controlled McKean–Vlasov dynamics." Ann. Probab. 43 (5) 2647 - 2700, September 2015. https://doi.org/10.1214/14-AOP946

Information

Received: 1 March 2013; Revised: 1 March 2014; Published: September 2015
First available in Project Euclid: 9 September 2015

zbMATH: 1322.93103
MathSciNet: MR3395471
Digital Object Identifier: 10.1214/14-AOP946

Subjects:
Primary: 93E20
Secondary: 60H10, 60K35

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 5 • September 2015
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