Order Book Dynamics and Price Impact in Limit Order Markets

We study the dynamics of a continuous-time limit order book model in which market orders arrive as Poisson processes and the mid-price evolves as a diffusion driven by order-flow imbalance. Price impact is decomposed into a temporary component and a permanent component that shifts the fundamental value. Using a Hamilton–Jacobi–Bellman framework we derive the optimal liquidation strategy for a large trader minimising expected execution cost subject to a terminal inventory constraint, obtaining a closed-form feedback control in the linear–quadratic case and a numerical solution via backward Euler for nonlinear impact functions.