The mean-field term causes nontrivial troubles in the classical method by the Riccati equation
Research gap analysis derived from 3 mathematics papers in our local library.
The gap
The mean-field term causes nontrivial troubles in the classical method by the Riccati equation. There is no result to connect optimal solutions of stochastic control problems on infinite horizon with the periodic measures.
Evidence profile
Sourced from the stated research gap of the source papers, classified as general, spanning 3 journals.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 3 representative gaps
- The ergodic linear-quadratic optimal control problems for stochastic mean-field systems with periodic coefficients (2026) · ESAIM Control Optimisation and Calculus of Variations · doi
The mean-field term causes nontrivial troubles in the classical method by the Riccati equation. There is no result to connect optimal solutions of stochastic control problems on infinite horizon with the periodic measures.
generalstated research gapevidence 5/5Keywords: mean-field term causes nontrivial troubles classical method riccati - Mean-Field Singular Stochastic Control with Regime Switching: Maximum Principles and Application (2026) · Risks · doi
The lack of a comprehensive framework for solving mean-field singular stochastic optimal control problems with regime switching. The need for a framework that can handle regime shifts and singular controls. The absence of a stochastic maximum principle for this class of problems.
generalstated research gapevidence 5/5Keywords: lack comprehensive framework solving mean-field singular stochastic optimal - Mean-Field Limit for Stochastic Control Problems under State Constraint (2026) · SIAM Journal on Control and Optimization · doi
Mean-field control problems with state constraints have not been thoroughly studied. The existing literature has not provided a comprehensive study of the convergence problem of mean-field control theory in the presence of state constraints and nondegenerate idiosyncratic noise. The paper seeks to fill this gap by providing a thorough study of the convergence problem.
generalstated research gapevidence 5/5Keywords: mean-field control problems state constraints have been thoroughly
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