Establishes existence of optimal controls for constrained mean-field problems with singular controls and derives associated SMP and constrained FBSDEs using relaxed formulation and Lagrange multipliers.
Extended mean-field control problems with Poissonian common noise: Stochastic maximum principle and Hamiltonian-Jacobi-Bellman equation
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
This paper studies mean-field control problems with state-control joint law dependence and Poissonian common noise. We develop the stochastic maximum principle (SMP) and establish its connection to the Hamiltonian-Jacobi-Bellman (HJB) equation on the Wasserstein space. The presence of the conditional joint law and its discontinuity under Poissonian common noise bring new technical challenges. To develop the SMP when the control domain is not necessarily convex, we first consider a strong relaxed control formulation that allows us to perform the first-order variation. We propose the technique of extension transformation to overcome the compatibility issues arising from the joint law in the relaxed control formulation. By further establishing the equivalence between the relaxed control and the strict control formulations, we obtain the SMP for the original problem with strict controls. In the part to investigate the HJB equation, we formulate an equivalent controlled Fokker-Planck problem subjecting to a controlled measure-valued dynamics with Poisson jumps, which allows us to derive the HJB equation of the original problem under open-loop strict controls. We also establish the connection between the SMP and the HJB equation.
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UNVERDICTED 2representative citing papers
The paper derives the stochastic maximum principle for mean-field control under dynamic constraints by embedding the problem in Banach-space optimization and applying generalized Fritz-John conditions to obtain a BSDE as the Lagrange multiplier.
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Constrained mean-field control with singular controls: Existence, stochastic maximum principle and constrained FBSDE
Establishes existence of optimal controls for constrained mean-field problems with singular controls and derives associated SMP and constrained FBSDEs using relaxed formulation and Lagrange multipliers.
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Extended mean-field control under constraints: The generalized Fritz-John conditions and Lagrangian method
The paper derives the stochastic maximum principle for mean-field control under dynamic constraints by embedding the problem in Banach-space optimization and applying generalized Fritz-John conditions to obtain a BSDE as the Lagrange multiplier.