Mean Field Games and Mean Field Type Control Theory

By Alain Bensoussan, Jens Frehse, Phillip S. C. Yam. 2013

834 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/b0b30e4b010d167a6a80a54cf8c51b0ebdc8e29f

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Citations in the corpus

McKean–Vlasov optimal control: The dynamic programming principle (2019, background): “This was first achieved by Lauriére and Pironneau [56], and later by Bensoussan, Frehse, and Yam [10; 11; 12], who assumed the existence at all times of a density for the marginal distribution of the state process, and reformulated the problem as a deterministic density control problem, with a famil”
Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications (2016, neutral): “Optimal control of McKean-Vlasov equation is a rather new topic in the area of stochastic control and applied probability, and addressed, e.g., in [4], [11], [8], [15], [31].”
Finite state mean field games with Wright–Fisher common noise (2019, background): “For recent theoretical developments and applications of this theory, we refer the reader to [7, 4, 9, 10] and the references therein.”
Stationary focusing mean-field games (2016, background): “For a description and up-to-date developments on MFG we refer the reader to [3, 17, 6, 30].”
Mean field game of controls and an application to trade crowding (2016, background): “Since these pioneering works the literature on MFG has grown very fast: see for instance the monographs or the survey papers [Bensoussan et al., 2013, Caines, 2015, Gomes and Others, 2014].”
MEAN FIELD GAMES: A TOY MODEL ON AN ERDOS-RENYI GRAPH (2017, background): “Since then, alternative strategies, including probabilistic ones, have been suggested, see for instance [4] or the forthcoming monograph [5,6] together with the textbook [1].”
Mean–field moral hazard for optimal energy demand response management (2019, result): “The result is quite similar to those found in the literature onMcKean–Vlasov problems, see, for example„ Bensoussan, Frehse, and Yam (2013), Bensoussan, Frehse, and Yam (2015), Bensoussan, Frehse, and Yam (2017), Pham andWei (2018), Pham andWei (2017), Bayraktar, Cosso, and Pham (2018), or Djete et…”
Numerical method for FBSDEs of McKean–Vlasov type (2017, methodology): “We refer to our previous paper [20] for a complete overview on the subject, together with the references [8, 12, 17, 18, 19].”
Master Bellman equation in the Wasserstein space: Uniqueness of viscosity solutions (2021, background): “The topic of mean field optimal control is a very recent area of research, on which there are however already many papers and the two monographs [5, 14], to which we refer for a thorough introduction.”
Zero-sum stochastic differential games of generalized McKean–Vlasov type (2018, background): “1 Introduction McKean-Vlasov (McKV) control problem (also called mean-field type control problem) has been knowing a surge of interest with the emergence of mean-field game (MFG) theory, see [21], [5], [22], [10].”
Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource (2016, neutral): “For a comparison of mean field games and mean field type control, see the book of Bensoussan, Frehse, and Yam [8] as well as the article by Carmona, Delarue, and Lachapelle [23].”