arXiv subjects

Jingfei Wang

Publications and source records attributed to Jingfei Wang.

6 recordsLinked to original sources

arXiv2026

Mean Field Stackelberg Game for Production and Carbon Emission Reduction with State Reflections

Global warming, driven by anthropogenic carbon emissions with transboundary pollution characteristics and irreversible damage, poses an existential threat to human society. This paper develops a novel two-level Stackelberg game with mean field interaction of controls and common noise which integrates hierarchical decision-making under a state-reflected emission dynamics. A central regulator (leader) adjusts product prices to guide $n$ heterogeneous competing regions (followers) while enforcing a hard emission cap via a reflection mechanism that models emergency reductions through a local time process. We establish the existence of an approximate Stackelberg equilibrium and perform sensitivity analysis via Monte Carlo simulations.

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arXiv2025

Mean Field Control with Poissonian Common Noise: A Pathwise Compactification Approach

This paper contributes to the compactification approach to study mean-field control problems with Poissonian common noise. To overcome the lack of compactness and continuity issues caused by common noise, we exploit the point process representation of the Poisson random measure with finite intensity and propose a pathwise formulation in a two-step procedure by freezing a sample path of the common noise. In the first step, we establish the existence of optimal relaxed controls in the pathwise formulation as if common noise is absent, but with finite deterministic jumping times. The second step plays the key role in our approach, which is to aggregate the optimal solutions in the pathwise formulation over all sample paths of common noise and show that it yields an optimal solution in the original model. To this end, with the help of concatenation techniques, we first develop a pathwise superposition principle in the model with deterministic jumping times, drawing a relationship between the pathwise relaxed control problem and the pathwise measure-valued control problem. We then further bridge the equivalence among different problem formulations and verify that the constructed solution under aggregation is indeed optimal in the original problem.

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arXiv2025

Mean Field Game of Controls with State Reflections: Existence and Limit Theory

This paper studies mean field game (MFG) of controls by featuring the state-control joint distribution and the reflected state process at an exogenous stochastic reflection boundary. We contribute to the literature with a customized relaxed formulation and some new compactification arguments to establish the existence of a Markovian mean field equilibrium (MFE) in the weak sense. We consider an enlarged canonical space, utilizing the dynamic Skorokhod mapping, to accommodate the stochastic reflection boundary process. A fixed-point argument on the extended space using an extension transformation technique is developed to tackle challenges from the joint measure flow of the state and the relaxed control that may not be continuous. Furthermore, the bidirectional connections between the MFG and the $N$-player game are established. We first show that any weak limit of empirical measures induced by $\boldsymbol{\epsilon}$-Nash equilibria in $N$-player games must be supported exclusively on the set of relaxed mean field equilibria, analogous to the propagation of chaos in mean field control problems. We then prove the convergence result that a Markovian MFE in the weak sense can be approximated by a sequence of constructed $\boldsymbol{\epsilon}$-Nash equilibria in the weak sense in $N$-player games when $N$ tends to infinity.

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arXiv2025

Constrained mean-field control with singular controls: Existence, stochastic maximum principle and constrained FBSDE

This paper studies a class of mean-field control (MFC) problems with singular controls under general dynamic state-control-law constraints. We first propose a customized relaxed control formulation to cope with the dynamic mixed constraints and establish the existence of an optimal control using compactification argument in the proper canonical spaces to accommodate singular controls. To further characterize the optimal pair of regular and singular controls, we treat the controlled McKean-Vlasov process as an infinite-dimensional equality constraint and recast the MFC problem as an optimization problem on canonical spaces with constraints on Banach space, allowing us to derive the stochastic maximum principle (SMP) and a class of constrained BSDE using a new Lagrange multipliers method. Additionally, we investigate the uniqueness and the stability result of the solution to the constrained FBSDE associated with the constrained MFC with singular controls.

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arXiv2024

Extended mean-field control under constraints: The generalized Fritz-John conditions and Lagrangian method

This paper studies mean-field control with joint law dependence under dynamic expectation constraints and/or dynamic state-control-law constraints. We pioneer the establishment of the stochastic maximum principle (SMP) and the derivation of the backward SDE (BSDE) from the perspective of constrained optimization using the method of Lagrangian multipliers. We first propose to embed the constrained mean-field control (C-MFC) with joint-law dependence into some abstract optimization problems with constraints on Banach spaces, for which we develop the generalized Fritz-John (FJ) optimality conditions. We then prove the stochastic maximum principle (SMP) for C-MFC by transforming the FJ conditions into an equivalent stochastic first-order condition associated with a general type of constrained forward-backward SDEs (FBSDEs). Contrary to the existing literature, we treat the McKean-Vlasov SDE as an infinite-dimensional equality constraint such that the BSDE induced by the FJ first-order optimality conditions can be interpreted as the generalized Lagrange multiplier. We also employ the methodology to stochastic control and mean field game problems under dynamic constraints.

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arXiv2024

Extended mean-field control problems with Poissonian common noise: Stochastic maximum principle and Hamiltonian-Jacobi-Bellman equation

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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