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Optimal Market Making with Hawkes Process Dynamics: An Impulse Control Formulation

Naoki Takata
January 14, 2026

Abstract

We present a rigorous mathematical formulation of the optimal market making problem driven by multidimensional Hawkes processes under an impulse control framework. The model incorporates self-exciting order flow dynamics, inventory risk management, and strategic order placement. We derive the Hamilton-Jacobi-Bellman quasi-variational inequality (HJB-QVI) characterizing the value function and establish the terminal boundary condition for the optimization problem.

Paper

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Timestamp: January 14, 2026 (date recorded on the blockchain)

Contact

Naoki Takata
X: @naokitakata
Email: [ntakata [at] proton.me]

This is a preprint. Comments are welcome!