Paper: arXiv 2604.12114

Authors: Onésime Hounkpe, Dena Firoozi, Shuang Gao

Abstract

We propose a decomposition method for solving a general class of linear-quadratic (LQ) McKean-Vlasov control problems involving conditional expectations and random coefficients, where the system dynamics are driven by two independent Wiener processes. Unlike existing approaches in the literature for these problems, such as the extended stochastic maximum principle and the extended dynamic programming methods, which often involve additional technical complexities and sometimes impose restrictive conditions on control inputs, our approach decomposes the original McKean-Vlasov control problem into two decoupled stochastic optimal control problems, one of which has a constrained admissible control set. These auxiliary problems can be solved using classical methods. We establish an equivalence between the well-posedness and solvability of the auxiliary problems and those of the original problem, and show that the sum of the optimal controls of the auxiliary problems yields the optimal control of the original problem. Moreover, by applying a variational method, we characterize the optimal solution to the McKean-Vlasov control problem via two decoupled sets of (non-McKean-Vlasov) linear forward-backward stochastic differential equations, each corresponding to one of the auxiliary problems. Finally, we show that standard dynamic programming can also be applied to solve the resulting auxiliary problems.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated theoretical framework for Linear-Quadratic McKean-Vlasov control problems using FBSDEs and dynamic programming. However, it is purely mathematical without empirical validation or backtesting on real-world financial market data.

Research Flowchart

  flowchart TD
    A[Goal: Solve LQ Conditional McKean-Vlasov Control Problems with Random Coefficients] --> B[Inputs: System Dynamics driven by 2 Independent Wiener Processes & Random Coefficients]
    B --> C[Method: Decompose into 2 Decoupled Stochastic Optimal Control Problems]
    C --> D[Solve Auxiliary Problems via Variational Methods & Standard Dynamic Programming]
    D --> E[Outcome: Characterization via 2 Decoupled Linear FBSDEs]
    E --> F[Outcome: Sum of Auxiliary Optimal Controls Yields Original Optimal Control]

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0 of 54 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.