Optimal Order Placement in a Limit Order Book Model with State-Dependent Hawkes Processes

This study addresses the optimal quote placement problem for market makers, modeling order flow as a state-dependent Hawkes process. Combining a piecewise linear demand setting with a continuous-time discrete-state dynamic programming framework, it derives backward recursions for quadratic value function coefficients of inventory-dependent quotes under quadratic terminal inventory penalties. Numerical experiments based on LOBSTER data show that this strategy achieves higher total terminal wealth than fixed-spread benchmarks at 1 and 3 ticks, but lower at 2 ticks.