ABSTRACT

A fundamentally important problem in algorithmic trading is determining the optimal trading trajectory for a large trade during a finite horizon that minimizes a cost function that jointly models the effects of market impact and market risk. In this paper, we derive explicit formulas for the optimal implementation shortfall trading curve with linear and nonlinear market impact. A complete characterization of the solution and optimal trading trajectory is provided as a quadratic optimization problem. We also analyze how changing the risk aversion weight in the cost function modifies the optimal trading trajectories.