Optimal Trading: A Model Predictive Control Approach

We develop a dynamic trading strategy in the Linear Quadratic Regulator (LQR) framework. By including price mean-reversion signal into optimization program, environment where market impact is linear and stage costs are quadratic, we obtain an optimal curve that reacts opportunistically to changes while retaining its ability satisfy smooth or hard completion constraints. The allocation affine spot number of outstanding shares at any time, it can be fully derived iteratively. It also aggressive money, meaning accelerates whenever favorable, with intensity calibrated by practitioner. Since LQR may yield locally negative participation rates (i.e round trip trades) which often undesirable, show aforementioned problem improved solved under positivity constraints following Model Predictive Control (MPC) approach. In particular, smoother more consistent constraint than putting floor on rate. finally examine how simplified continuous context, allows us derive closed formula for further assumptions, document two-step case trades occur additional dark pool.