Wealth Taxation as a Drift Modification: A Fokker-Planck Approach to Tax Neutrality

Abstract

We reformulate the neutral wealth tax framework of Froeseth (2026; arXiv:2603.05264) in the language of stochastic dynamics and statistical physics. Individual wealth under geometric Brownian motion satisfies a Langevin equation with multiplicative noise; the probability density of wealth across a population then evolves according to a Fokker-Planck equation. A proportional wealth tax at market value enters as a uniform reduction of the drift coefficient, preserving the diffusion structure and all relative probability currents. This drift-shift symmetry is the physical content of tax neutrality. Each channel through which neutrality breaks down in practice - book-value assessment, liquidity frictions, forced dividend extraction, migration, and market impact - corresponds to a specific violation of this symmetry: a state-dependent, asset-dependent, or flow-dependent modification of the Fokker-Planck equation. The framework clarifies when wealth taxation is a benign rescaling of the dynamics and when it introduces genuinely new physics.

35 pages, 4 figures, 1 table. v3: Heston-section Brownian motions renamed and defined explicitly (W^(1,2) -> B^(1,2)), removing a notational collision with wealth W in eq. (31); bibliography updated with arXiv identifiers for companion papers. v2: sqrt(F) attribution corrected; Bernard et al. citation added