A General Stochastic Maximum Principle for SDEs of Mean-field Type

By Rainer Buckdahn, Boualem Djehiche, Juan Li. 2011

337 citations recorded by the source corpus.

Subfields: Demography, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/12899c7511f308627503d92194b98322eca0dbee

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Citations in the corpus

Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics (2013, background): “standard calculus chain rules; see, for example, [2, 4].”
A probabilistic weak formulation of mean field games and applications (2013, background): “Early forms of a stochastic maximum principle for this new type of control problem were given in [4, 7, 34].”
Mean-field stochastic linear quadratic optimal control problems: closed-loop solvability (2016, neutral): “See, for examples, McKean [16], Buckdahn–Djehiche–Li–Peng [5], Buckdahn–Li–Peng [6], Andersson–Djenhiche [2], Buckdahn–Djehiche–Li [4], Meyer-Brandis–Øksendal–Zhou [17], Yong [25], Elliott–Li–Ni [10], Cui–Li–Li [9], Huang–Li–Wang [11], Huang–Li–Yong [12].”
McKean–Vlasov optimal control: The dynamic programming principle (2019, background): “Andersson and Djehiche [3] and Buckdahn, Djehiche, and Li [19] use this approach for a specific case of optimal control of a McKean–Vlasov equation, corresponding to the case where the coefficients of the equation and the reward functions only depend on some moments of the law.”
Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations (2016, positive): “This naturally results in amean-field backward stochastic differential equation (MF-BSDE, for short) with a given terminal condition (see Buckdahn–Djehiche–Li–Peng [6] and Buckdahn–Li–Peng [7]).”
A mean-field stochastic control problem with partial observations (2017, background): “, φ·∧t = φt), then the problem becomes a stochastic control problem with McKean-Vlasov dynamics and/or a Mean-field game (see, for example, [7, 8, 9] in its “forward” form, and [2, 3, 4] in its “backward” form).”
Mean-field optimal control as Gamma-limit of finite agent controls (2018, methodology): “The most popular methods are based on extending Pontryagin’s maximum principle [2, 6, 9, 14, 17] or deriving a dynamic programming principle, and with it a form of a Hamilton-Jacobi-Bellman equation on a space of probability measures [8, 47, 54].”
A Stochastic Maximum Principle for General Mean-Field Systems (2016, methodology): “Furthermore, the processes (p, q) and (P, Q) are the solutions of the first and second order adjoint equations that are in the form of mean-field backward SDEs similar to those in [3], but the parts involving second order derivatives require special attention.”