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

Battle Count: 92

Highly relevant to quantitative trading in DeFi and privacy-preserving exchange contexts. The paper provides closed-form formulas for price impact (lambda), insider trading intensity (beta), and the cumulative privacy subsidy, all directly applicable to fee calibration and LP pool management. The LVR bridge connects to the CFMM/AMM literature central to DeFi quantitative strategies. The break-even fee formula f >= sigma_v*sigma_epsilon^2/(Q*sqrt(sigma_u^2+sigma_epsilon^2)) is directly implementable. However, the paper is theoretical and does not provide trading signals or backtestable strategies.

The theoretical framework requires understanding of continuous-time stochastic calculus (Ito integrals, Brownian motions), Bayesian filtering (Kalman gain), HJB optimization, and market microstructure theory. The closed-form results are elegant but the derivation involves multiple coupled ODEs (Riccati equation for posterior variance, HJB for insider). Practical implementation for DeFi fee calibration is moderate: the break-even fee formula is a simple closed-form expression. The discrete-block interpretation (Section 6.1) adds engineering complexity for actual protocol deployment. The DP feasibility mapping (Section 6.1) requires additional cryptographic expertise.

The paper provides complete analytical proofs (Theorems 1-2, Proposition 1, Corollary 1) with detailed proof sketches. All equilibrium objects (lambda, beta, Sigma) are given in closed form. The welfare decomposition is fully specified. However, no numerical simulations or code are provided. The model is entirely theoretical with well-defined primitives, making analytical reproduction straightforward. The companion paper [13] provides the single-period baseline.