A Maximum Principle for SDEs of Mean-Field Type

By Daniel Andersson, Boualem Djehiche. 2011

406 citations recorded by the source corpus.

Subfields: Demography, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/d903d074df36d1016dea8683b76abaea152b69f4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Demography

In Economics and Econometrics

In Finance

Citations in the corpus

Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations (2016, neutral): “Typical representatives include, but not limited to, McKean [27], Dawson [15], Chan [12], Buckdahn–Djehiche–Li–Peng [6], Buckdahn–Li–Peng [7], Borkar–Kumar [5], Crisan–Xiong [14], Andersson–Djehiche [2], Buckdahn–Djehiche–Li [8], MeyerBrandis–Oksendal–Zhou [28], Yong [35,36], Huang–Li–Yong [20], Li–”
Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications (2016, background): “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].”
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 Mean Field Games (2014, background): “If one considers a system of interacting particles under centralized control, instead of one in which every particle having the free will to choose its own control as formulated in MFGs, a stochastic control problem of mean field type would result (see [31,47] and [33]).”
Control of McKean–Vlasov dynamics versus mean field games (2012, background): “On the other hand, as we explained in the special case of scalar interactions derived from [1], the forward-backward system associated with the MKV control problem involves additional terms coming from the need to optimize with respect to the interaction terms.”
A General Stochastic Maximum Principle for SDEs of Mean-field Type (2011, result): “A partial result in this direction was obtained independently by Li [14] and Andersson and Djehiche [ 2 ], when the action space U”
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: Open-Loop Solvabilities (2015, neutral): “Control problems of MF-SDEs were studied by Ahmed–Ding [3], Ahmed [1], Park–Balasubramaniam–Kang [23], Buckdahn–Djehiche–Li [6], Andersson–Djehiche [4], Meyer-Brandis–Øksendal–Zhou [22], and so on.”
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].”
A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations (2011, background): “More interestingly, control problems of McKean–Vlasov equation or MF-FSDEs were investigated by Ahmed–Ding [2], Ahmed [3], Buckdahn–Djehiche–Li [7], Park–Balasubramaniam–Kang [28], Andersson–Djehiche [4], Meyer-Brandis– Oksendal–Zhou [25], and so on.”
A mean-field stochastic maximum principle via Malliavin calculus (2012, background): “one that is similar to the adjoint equation in [1].”
Bellman equation and viscosity solutions for mean-field stochastic control problem (2015, positive): “…solutions to the controlled McKean − Vlasov systems in terms of an adjoint backward stochastic diﬀerential equation (BSDE) coupled with a forward SDE: see [3,9,38] with a state dynamics depending upon moments of the distribution, and [13] for a deep investigation in a more general setting.”
Robust Markowitz mean‐variance portfolio selection under ambiguous covariance matrix (2016, positive): “It has then been solved in [2] where the authors have derived a version of the Pontryagin maximum principle.”
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].”