Structural Hawkes Ambiguity in Near-Critical Market Making

This paper studies a narrow source of model risk in market making: uncertainty about the self-excitation structure of Hawkes order flow. The structure is encoded by a branching matrix Gamma, while the distance to instability is measured by the Perron root rho(Gamma). In a reduced robust inventory model, ambiguity in Gamma is amplified through the Hawkes resolvent (I - Gamma)^(-1), so near-critical calibration error can become an economic risk premium. The critical exponent depends on normalization: relative critical-slack ambiguity gives a square-law reduced premium, while absolute branching-matrix ambiguity contributes one additional derivative factor when epsilon = o(1 - rho). The paper gives a reduced-form spectral theorem and conditional robust-control bridges under stated compact-PDMP, Lyapunov, weighted-comparison, and smooth-interior assumptions. It then evaluates robust and nominal quoting policies under common random numbers, Ogata event times, public LOBSTER sample replays, Binance aggregate trades, and crypto order-book samples. The empirical claim is deliberately limited: structural Hawkes ambiguity is visible in these near-critical stress tests, but public Hawkes calibrations remain diagnostic inputs rather than complete execution models.