Optimal liquidation under indirect price impact with propagator

We propose in this paper a new framework of optimal liquidation strategies for a trader seeking to liquidate his large inventory based on a jump-dependent price impact model with propagator. This new jump-dependent price impact model best reproduces the empirical direct and indirect effects of market orders on the transaction price. More precisely, different choices of propagators are proposed and their implications in terms of temporary, permanent and transient impacts on the transaction price are discussed. For each choice of such kernels, we formulate the most relevant optimal liquidation problem faced by the trader, derive explicitly the related Hamilton-Jacobi-Bellman equation and solve it numerically. We then also show how our price impact model can be extended to incorporate the use of limit orders by the liquidating trader. Therefore, we aim with this paper to propose an alternative, more realistic and flexible description of the order book's dynamic, thereby contributing to bridging the gap between high-frequency price models and optimal liquidation problems.