Optimal Order Placement under a State-Dependent Hawkes Process Limit Order Book model

Abstract

We study optimal quote placement for a market maker facing order flow modeled by a state-dependent Hawkes process. A block-based linear demand specification links market-order counts to execution volumes, providing the demand moments required by a continuous time discrete state dynamic programming formulation. Under a quadratic terminal inventory penalty, we characterize inventory-dependent quotes and derive backward recursions for the coefficients of a quadratic value function. Numerical experiments using LOBSTER data examine quote distributions, inventory exposure, and terminal wealth. The implemented strategy yields higher aggregate terminal wealth than fixed-spread benchmarks at one and three ticks, but lower wealth than the two-tick benchmark. These results illustrate the framework's numerical implementation and distinguish terminal-wealth comparisons from evaluation under the inventory-penalized objective.