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

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  • Yuki Nakamura

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 $\sigma_\varepsilon$. Under the Markovian linear equilibrium, the price-impact coefficient is $\lambda = \sigma_v / \sqrt{\sigma_u^2 + \sigma_\varepsilon^2}$ -- constant in time -- and the cumulative expected transfer from the protocol's liquidity pool to traders over $[0,1]$ is $|\Pi_M| = \sigma_v \sigma_\varepsilon^2 / \sqrt{\sigma_u^2 + \sigma_\varepsilon^2}$. 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.

Suggested Citation

  • Yuki Nakamura, 2026. "The Privacy Subsidy in Continuous-Time Kyle: Cumulative Welfare under Noise-Perturbed Order-Flow Observation," Papers 2605.25631, arXiv.org, revised May 2026.
    • Handle: RePEc:arx:papers:2605.25631
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    References listed on IDEAS

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