From Gravity to Confinement: Wealth Redistribution as Optimal Drift Design in the Fokker–Planck Framework

Battle Count: 75

The paper is primarily about wealth taxation policy design and wealth distribution dynamics, not about trading strategies or market microstructure. However, it has tangential relevance: (1) the Fokker–Planck / SDE framework is the same mathematical language used in quantitative finance for asset pricing and risk modelling; (2) the drift-diffusion decomposition of wealth dynamics parallels return modelling; (3) the spectral gap analysis informs how quickly wealth distributions respond to shocks, relevant for long-horizon portfolio allocation; (4) the general equilibrium feedback (tax → capital stock → returns) affects the risk-free rate and equity premium assumptions used in trading models. The paper does not propose any trading signals, execution algorithms, or alpha-generating strategies.

The theoretical framework involves: (1) solving Fokker–Planck PDEs with state-dependent drift; (2) spectral analysis of the FP operator for convergence rates; (3) Pontryagin maximum principle for optimal control of PDEs (forward-backward coupled systems); (4) McKean–Vlasov self-consistency requiring fixed-point iteration; (5) numerical PDE methods for the general nonlinear case. The closed-form results (Gini formulas, Pareto exponent, OU steady state) are straightforward, but the full optimal control problem and GE extension require significant numerical expertise. Empirical implementation via neural SDEs adds further complexity.

The paper is primarily theoretical with closed-form analytical results (Propositions 1 and 2, Gini formulas, Pareto exponent derivation). All key equations are self-contained. However, no code or numerical simulations are provided. Empirical validation is deferred to a companion paper. The mathematical derivations are complete and verifiable, but the optimal control solution requires numerical PDE methods not detailed here.