McKean-Vlasov optimal control: the dynamic programming principle
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Publication:2129699
DOI10.1214/21-AOP1548zbMath1491.49018arXiv1907.08860OpenAlexW2963164374MaRDI QIDQ2129699
Mao Fabrice Djete, Xiaolu Tan, Dylan Possamaï
Publication date: 22 April 2022
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1907.08860
Dynamic programming in optimal control and differential games (49L20) Dynamic programming (90C39) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Optimal stochastic control (93E20) Applications of stochastic analysis (to PDEs, etc.) (60H30) Existence of optimal solutions to problems involving randomness (49J55)
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Cites Work
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- Control of McKean-Vlasov dynamics versus mean field games
- Mimicking an Itō process by a solution of a stochastic differential equation
- Superreplication under volatility uncertainty for measurable claims
- A theory of Markovian time-inconsistent stochastic control in discrete time
- Mean field games with common noise
- On time-inconsistent stochastic control in continuous time
- On the robust superhedging of measurable claims
- Mean field games
- Functional analysis, Sobolev spaces and partial differential equations
- Stochastic optimal control. The discrete time case
- Martingale problems for conditional distributions of Markov processes
- Stochastic control for a class of nonlinear kernels and applications
- Dynamic programming for stochastic target problems and geometric flows
- Viscosity solutions to parabolic master equations and McKean-Vlasov SDEs with closed-loop controls
- Quenched mass transport of particles toward a target
- Zero-sum stochastic differential games of generalized McKean-Vlasov type
- The master equation in mean field theory
- On the interpretation of the master equation
- Constructing sublinear expectations on path space
- A Pseudo-Markov Property for Controlled Diffusion Processes
- Nonlinear Lévy processes and their characteristics
- Superhedging and Dynamic Risk Measures under Volatility Uncertainty
- Bellman equation and viscosity solutions for mean-field stochastic control problem
- Dynamic Programming for Controlled Markov Families: Abstractly and over Martingale Measures
- Viscosity Solutions for Controlled McKean--Vlasov Jump-Diffusions
- Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics
- Compactification methods in the control of degenerate diffusions: existence of an optimal control
- Mean Field Games and Mean Field Type Control Theory
- Limit Theory for Controlled McKean--Vlasov Dynamics
- The Master Equation for Large Population Equilibriums
- Dynamic Programming for Optimal Control of Stochastic McKean--Vlasov Dynamics
- Dynamic programming for mean-field type control
- Optimal Transport
