The Privacy Subsidy in Continuous-Time Kyle: Cumulative Welfare under Noise-Perturbed Order-Flow Observation

• URL: http://arxiv.org/abs/2605.25631v4
• Date: Sun, 31 May 2026 05:56:52 GMT
• Title: The Privacy Subsidy in Continuous-Time Kyle: Cumulative Welfare under Noise-Perturbed Order-Flow Observation
• Abstract summary: We extend the closed-form privacy-subsidy result of Nakamura (2026, arXiv05.15746) from the single-period Kyle model to continuous-time.<n>We establish a structural correspondence between this cumulative privacy subsidy and Loss-Versus-Rebalancing.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We extend the closed-form privacy-subsidy result of Nakamura~(2026, arXiv:2605.15746) from the single-period Kyle model to continuous-time. A committed Bayesian automated market maker observes the aggregate order flow perturbed by an independent Brownian privacy channel of diffusion intensity $σ_\varepsilon$. Under the Markovian linear equilibrium, the price-impact coefficient is $λ= σ_v / \sqrt{σ_u^2 + σ_\varepsilon^2}$ -- constant in time -- and the cumulative expected transfer from the protocol's liquidity pool to traders over $[0,1]$ is $|Π_M| = σ_v σ_\varepsilon^2 / \sqrt{σ_u^2 + σ_\varepsilon^2}$. We then establish a structural correspondence between this cumulative privacy subsidy and Loss-Versus-Rebalancing (Milionis et al.~2022), identifying privacy-noise welfare as the order-flow observation analog of LVR's price observation gap. The result completes the continuous-time Kyle leg of the program of quantifying break-even fees for committed-AMM exchanges under privacy-aggregated information environments.

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