arXiv subjects

Anders G Frøseth

Publications and source records attributed to Anders G Frøseth.

10 recordsLinked to original sources

arXiv2026

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

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.

physics.soc-ph↗

arXiv2026

Spectral Portfolio Theory: From SGD Weight Matrices to Wealth Dynamics

We develop spectral portfolio theory by establishing a direct identification: neural network weight matrices trained on stochastic processes are portfolio allocation matrices, and their spectral structure encodes factor decompositions and wealth concentration patterns. The three forces governing stochastic gradient descent (SGD) - gradient signal, dimensional regularisation, and eigenvalue repulsion - translate directly into portfolio dynamics: smart money, survival constraint, and endogenous diversification. The spectral properties of SGD weight matrices transition from Marchenko-Pastur statistics (additive regime, short horizon) to inverse-Wishart via the free log-normal (multiplicative regime, long horizon), mirroring the transition from daily returns to long-run wealth compounding. We unify the cross-sectional wealth dynamics of Bouchaud and Mezard (2000), the within-portfolio dynamics of Olsen et al. (2025), and the scalar Fokker-Planck framework via a common spectral foundation. A central result is the Spectral Invariance Theorem: any isotropic perturbation to the portfolio objective preserves the singular-value distribution up to scale and shift, while anisotropic perturbations produce spectral distortion proportional to their cross-asset variance. We develop applications to portfolio design, wealth inequality measurement, tax policy, and neural network diagnostics. In the tax context, the invariance result recovers and generalises the neutrality conditions of Froseth (2026).

q-fin.PM↗

arXiv2026

Heterogeneous Returns and Wealth Tax Neutrality: A Fokker-Planck Framework

We extend the Fokker-Planck framework of Froseth (2026, arXiv:2603.05283) to populations of investors with heterogeneous, persistent return-generating ability. When the drift coefficient in the Langevin equation for log-wealth varies across investors, the proportional wealth tax remains a uniform drift shift but ceases to be neutral in the economic sense: its real incidence differs across ability types, and the stationary wealth distribution changes shape. We derive the extended Fokker-Planck equation on the joint space of log-wealth and ability, characterise the conditions under which the drift-shift symmetry breaks, and identify the consequences for asset prices and portfolio allocations. The analysis connects the neutrality results of Froseth (2026, arXiv:2603.05264) and the Fokker-Planck dynamics of Froseth (2026, arXiv:2603.05283) to the heterogeneous-returns literature, notably the "use-it-or-lose-it" mechanism of Guvenen, Kambourov, Kuruscu, Ocampo-Diaz and Chen (2023).

physics.soc-ph↗

arXiv2026

Minimum-Distortion Wealth Taxation, I: Information-Theoretic versus Transport-Geometric Optimality on the Proportional Class

We characterise minimum-distortion wealth taxation under two contrasting normative criteria within a Fokker-Planck framework on log-wealth: the JKO free-energy gap, an information-theoretic measure aligned with the Mirrleesian decision-distortion tradition, and the squared 2-Wasserstein distance from the no-tax distribution at horizon $T$, a transport-geometric measure aligned with the Saez-Zucman distributional-compression tradition. Restricting to the neutrality-preserving (C1)-(C3) schedule class of a companion paper (Froseth 2026), both optima admit closed forms in the two-dimensional design plane parametrised by the corporate-dividend retention $k = (1-τ_c)(1-τ_d)$ and the proportional wealth-tax rate $τ_w$. The JKO optimum partitions the regime axis into three phases as a function of the dimensionless ratio $ρ= Σ_0 m_0/σ^2$, with $m_0 = μ- σ^2/2$ the geometric mean log-return: a pure wealth-tax phase at low $ρ$, a mixed-instrument phase at intermediate $ρ$, and a pure flow-tax phase at high $ρ$. The $W_2$ optimum, by contrast, is degenerate in this calibration: it pins to the pure flow-tax corner across the whole regime axis. The criterion contrast admits an economically meaningful reading via a bluntness index $B(m_0) = b/(a m_0)$ that measures the wealth-tax channel's mean-displacement-per-revenue overshoot relative to the flow-tax channel; JKO weights $B$ linearly, $W_2$ weights it quadratically, and the two normative traditions correspond to this difference in weighting. Norwegian-flavoured calibrations sit inside the JKO mixed-instrument phase under stock-heavy portfolio volatility but move into the pure flow-tax phase under the realised effective volatility of typical real-estate-heavy households.

physics.soc-ph↗

arXiv2026

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

A proportional wealth tax acts as a uniform gravitational field on the wealth distribution: it shifts the drift of the Fokker-Planck equation without altering the diffusion, preserving the Gini coefficient at all finite times. The same drift-shift symmetry that makes the tax non-distortionary also makes it non-redistributive through the market channel. Redistribution requires breaking this symmetry. A progressive tax (confining potential) replaces the Pareto steady state with a thinner-tailed distribution whose Gini is a closed-form function of the progressivity parameter; source-sink terms (tax-funded transfers) reshape the density directly. We formulate optimal redistribution as a control problem for the Fokker-Planck equation, penalising intervention costs including migration, evasion, and portfolio distortion. In general equilibrium the tax design feeds back through aggregate capital and the production function, yielding a self-consistent McKean-Vlasov equation with diminishing returns to progressivity. The spectral gap of the Fokker-Planck operator determines convergence speed: progressive taxes redistribute within policy-relevant timescales, whereas proportional taxes rely on slow demographic turnover.

physics.soc-ph↗

arXiv2026

A Spectral Generalisation of the Variance Ratio: Eigenstructure of Long-Horizon Portfolio Covariance and a Multi-Memory Factor Model of U.S. Equity Returns

We propose a multivariate generalisation of the Lo-MacKinlay (1988) variance ratio that decomposes long-horizon equity-return dynamics into separate return-channel and volatility-channel memory components across the cross-section of asset returns. The framework identifies a parsimonious five-factor model - capturing persistent, antipersistent, and multi-scale memory in returns and volatility - that fits four U.S. portfolio panels (the Fama-French 49-industry universe, its pre/post-1998 halves, and the Fama-French 100 size x book-to-market sort) and a European replication (Fama-French Europe 25), recovering seven stylised facts of long-horizon equity dynamics simultaneously across all five panels. Three findings carry economic content. (i) The same five-factor decomposition fits all five panels, indicating a cross-sectional structure robust to industry vs. size-and-value sorts, to sub-periods, and to U.S. vs. developed-European markets. (ii) U.S. equity volatility memory underwent a regime transition in the late 1980s - not at the static 1998 split-half boundary - with the slowest component of the volatility cascade lengthening from approximately two to four years; a 1000-replicate rolling-window bootstrap localises the transition with strictly non-overlapping 90% confidence bands separating pre- and post-transition windows. (iii) The cross-sectional loadings driving return-channel long memory are economically distinct from those driving volatility-channel cascade memory: a cross-channel beta-inversion test finds no panel with the positive alignment a single shared loading predicts, rejecting the shared-loading hypothesis toward anti-alignment on the two largest panels at Bonferroni p = 0.0004. Characteristics that predict return-momentum patterns therefore need not predict volatility-persistence patterns.

q-fin.ST↗

arXiv2026

Tax Migration as Social Contagion: A Tipping-Point Model with Application to the Scandinavian Wealth Tax Debate

Blandhol (2025) estimates that wealth-tax-induced emigration from Norway reduces long-run GDP by 1.3%. Dansk Industri scaled this figure to argue that a Danish wealth tax would cost billions - a claim central to the 2026 Danish election campaign. We develop a social contagion model in which the emigration rate depends on a visibility-weighted fraction of prior emigrants, producing tipping-point dynamics. Embedding the model in the Fokker-Planck framework of Froseth (2026, arXiv:2603.05283), we show that the micro-to-macro extrapolation underlying the 1.3% figure requires five identification conditions to hold simultaneously - each of which is violated. Using a panel of the 400 wealthiest Norwegians (2011-2025), we estimate the Pareto tail exponent (approximately 1.3, stable across years), identify the emigrants within Blandhol's 2016-2020 sample window, and document a hidden channel of heir-emigration - 36 recent cases carrying approximately 127 bn NOK - invisible in panel data because controlling owners retain their A-shares while heirs emigrate with economic exposure only. The event-study sample is dominated by passive wealth-holders with near-zero productivity haircuts, and the wealth-weighted integral that determines the GDP effect is controlled by individuals entirely absent from the sample. The Norwegian emigration wave is a non-scalable, path-dependent tipping event, not a smooth elasticity.

physics.soc-ph↗

arXiv2026

Extensions to the Wealth Tax Neutrality Framework

Frøseth (2026; arXiv:2603.05264) shows that a proportional wealth tax on market values is neutral with respect to portfolio choice, Sharpe ratios, and equilibrium prices under CRRA preferences and geometric Brownian motion. This paper investigates the robustness of that result along two dimensions. First, we extend the neutrality frontier: portfolio neutrality -- including all intertemporal hedging demands -- is preserved under stochastic volatility (Heston and general Markov diffusions) and Epstein-Zin recursive utility, but breaks under non-homothetic preferences such as HARA. Second, we identify four channels through which implemented wealth taxes depart from neutrality even under CRRA: non-uniform assessment across asset classes, general equilibrium price effects in inelastic markets, progressive threshold structures, and endogenous labour supply. Each channel is formalised and, where possible, calibrated to the Norwegian wealth tax system. The progressive threshold introduces a tax shield that increases risk-taking near the exemption boundary -- an effect opposite in sign to the HARA distortion -- and, at the extreme, generates a participation margin at which investors exit the tax jurisdiction entirely. We formalise this tax-induced migration as the extreme response at the progressive threshold and examine the Norwegian post-2022 experience as a case study. The full framework is applied to evaluate the Saez-Zucman proposal for a global minimum wealth tax on billionaires and the related French proposal for a national minimum tax above EUR 100 million.

physics.soc-ph↗

arXiv2026

Flow Taxes, Stock Taxes, and Portfolio Choice: A Generalised Neutrality Result

A proportional wealth tax - a levy on the stock of wealth - preserves portfolio neutrality by acting as a uniform drift shift in the Fokker-Planck equation for wealth dynamics. We extend this result to the full system of ownership taxes (eierkostnader) that a shareholder faces: a corporate tax on gross profits, a capital income tax on the risk-free return, a dividend and capital gains tax on the excess return, and a wealth tax on net assets. Each tax modifies the drift of the wealth process in a distinct way - multiplicative rescaling, constant shift, or regime-dependent compression - while leaving the diffusion coefficient unchanged. We show that the combined system preserves portfolio neutrality under three conditions: (i) the capital income tax rate equals the corporate tax rate, (ii) the shielding rate equals the risk-free rate, and (iii) the wealth tax assessment is uniform across assets. When these conditions hold, the after-tax excess return is a uniform rescaling of the pre-tax excess return by the factor $(1-τ_c)(1-τ_d)$, and the drift-shift symmetry of the wealth-tax-only case generalises to a drift-shift-and-rescale symmetry. We classify the distortions that arise when each condition fails and show that flow-tax distortions and stock-tax distortions are additively separable: they do not interact. The shielding deduction - a feature of several real-world tax systems, including the Norwegian aksjonaermodellen - emerges as the mechanism that restores the symmetry between equity and debt taxation within this framework. Calibrated to the Norwegian dual income tax, conditions (i) and (ii) hold by institutional design; the only binding distortion is non-uniform wealth tax assessment, which generates portfolio tilts roughly 300 times larger than any residual flow-tax channel.

physics.soc-ph↗

arXiv2026

Asset Returns, Portfolio Choice, and Proportional Wealth Taxation

We analyse the effect of a proportional wealth tax on asset returns, portfolio choice, and asset pricing. The tax is levied annually on the market value of all holdings at a uniform rate. We show that such a tax is economically equivalent to the government acquiring a proportional stake in the investor's portfolio each period -- a form of risk sharing in which expected wealth and risk are reduced by the same factor, while the return per share is unaffected. This multiplicative separability drives four main results. First, the coefficient of variation of wealth is invariant to the tax rate. Second, the optimal portfolio weights -- and in particular the tangency portfolio -- are independent of the tax rate. Third, the wealth tax is orthogonal to portfolio choice: it induces a homothetic contraction of the opportunity set in the mean-standard deviation plane that preserves the Sharpe ratio of every portfolio. Fourth, both taxed and untaxed investors are willing to pay the same price per share for any asset. The results are derived first under geometric Brownian motion and then generalised to any return distribution in the location-scale family. A complementary Modigliani-Miller analysis confirms pricing neutrality and identifies an inconsistency in the existing literature regarding the discount rate used for after-tax cash flows. Imposing the CAPM as a special case confirms that after-tax betas equal pre-tax betas and the security market line contracts uniformly by $(1-τ_w)$; under CRRA preferences, general-equilibrium returns and prices are unchanged. This resolves an error in Fama (2021). The neutrality results depend on universal taxation at market value and frictionless markets. We formalise three channels -- book-value taxation, liquidity frictions, and dividend extraction -- through which these conditions break neutrality.

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