Optimal Execution : Linear Market Impact with Exponential Decay

Optimal execution of portfolio transactions is the essential part of algorithmic trading. The main result of this paper is the analytical equationfor the optimal trading trajectories with the assumption of exponential market recovery and short-time investment horizon. The formula has the same form and as simple as well known solution by GKAC ( R. Grinold and R. Kahn, R.Almgren and N.Chriss) but much more flexible. Also it is free of such undesirable features as infinite impact for finite discrete trades and instantaneous market recovery. In this revision we corrected typos and added appendix with illustrations of main equation