Infinite-Dimensional LQ Mean Field Games with Common Noise: Small and Arbitrary Finite Time Horizons

Battle Count: 75

The paper is highly relevant to quantitative finance at a theoretical level. MFGs with common noise directly model scenarios where all market participants are affected by macroeconomic shocks (monetary policy, systemic events). The infinite-dimensional framework enables modeling non-Markovian dynamics relevant to delayed systems in trading. However, the paper is purely theoretical with no numerical implementations, backtests, or direct trading strategies. The epsilon-Nash property provides justification for using MFG equilibria as approximations to finite-player games, which is foundational for algorithmic trading models. Applications to systemic risk, optimal execution, and portfolio trading are mentioned but not developed numerically.

Extremely high complexity. The paper deals with infinite-dimensional stochastic analysis in separable Hilbert spaces, requiring knowledge of C0-semigroups, Yosida approximations, operator-valued Riccati equations, Hilbert-Schmidt operators, trace-class operators, and mild vs. strong solutions of stochastic evolution equations. The decoupling field approach for FBSEEs with only mild solutions is technically demanding. Practical implementation would require significant expertise in functional analysis and stochastic PDEs. No computational framework is provided.

This is a purely theoretical mathematics paper with complete proofs provided. No computational experiments, code, or numerical results are presented. Reproducibility is limited to verifying the mathematical proofs. The paper builds on prior work [40] and [41] and uses standard tools from stochastic analysis in Hilbert spaces.