Forward-backward stochastic differential equations and controlled McKean-Vlasov dynamics
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Publication:888538
DOI10.1214/14-AOP946zbMATH Open1322.93103arXiv1303.5835OpenAlexW1820663283MaRDI QIDQ888538
Author name not available (Why is that?)
Publication date: 30 October 2015
Published in: (Search for Journal in Brave)
Abstract: The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the 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 games with mean field interactions.
Full work available at URL: https://arxiv.org/abs/1303.5835
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