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Bellman equation and viscosity solutions for mean-field stochastic control problem
15 references·9 citing·34 second hop
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References

  • 1999Continuous Martingales and Brownian Motion6,200 cited
  • 2007Mean field games2,638 cited
  • 2006Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle1,574 cited
  • 2000Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework1,009 cited
  • 2013Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations333 cited
  • 2010A Maximum Principle for SDEs of Mean-Field Type330 cited
  • 2017On time-inconsistent stochastic control in continuous time325 cited
  • 2011A General Stochastic Maximum Principle for SDEs of Mean-field Type281 cited
  • 2017Mean-field stochastic differential equations and associated PDEs275 cited
  • 2015Forward–backward stochastic differential equations and controlled McKean–Vlasov dynamics244 cited
  • 2015Mean Field Games and systemic risk244 cited
  • 2012Control of McKean–Vlasov dynamics versus mean field games238 cited
  • 2015Linear-Quadratic Mean Field Games233 cited
  • 2022A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria147 cited
  • 2014The Master equation in mean field theory

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138 cited

Cited by

  • 2019Mean-field optimal control as Gamma-limit of finite agent controls74 cited
  • 2019Extended Mean Field Control Problems: Stochastic Maximum Principle and Transport Perspective69 cited
  • 2022McKean–Vlasov optimal control: The dynamic programming principle67 cited
  • 2020Viscosity solutions to parabolic master equations and McKean–Vlasov SDEs with closed-loop controls49 cited
  • 2019Numerical method for FBSDEs of McKean–Vlasov type47 cited
  • 2022McKean–Vlasov Optimal Control: Limit Theory and Equivalence Between Different Formulations46 cited
  • 2020Viscosity Solutions for Controlled McKean--Vlasov Jump-Diffusions44 cited
  • 2020Mean–field moral hazard for optimal energy demand response management43 cited
  • 2019Schauder Estimates for a Class of Potential Mean Field Games of Controls33 cited