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.

翻译：我们将中村(2026, arXiv:2605.15746)中关于隐私补贴的闭式解结果从单期凯尔模型推广至连续时间。一个承诺型贝叶斯自动做市商观察到被独立布朗运动隐私信道（扩散强度$σ_\varepsilon$）扰动的总订单流。在马尔可夫线性均衡下，价格影响系数为$λ= σ_v / \sqrt{σ_u^2 + σ_\varepsilon^2}$——该系数随时间恒定——且协议流动性池在$[0,1]$上向交易者的累积期望转移为$|Π_M| = σ_v σ_\varepsilon^2 / \sqrt{σ_u^2 + σ_\varepsilon^2}$。我们进一步建立了该累积隐私补贴与"损失-再平衡"（Milionis et al. 2022）之间的结构对应关系，将隐私噪声福利识别为LVR中价格观测差距在订单流观测下的类比。该成果完善了在隐私聚合信息环境下量化承诺型AMM交易所盈亏平衡费用的连续时间凯尔模型分支研究。