Optimal trade execution under price-sensitive risk preferences

We consider the problem of how to close a large asset position in an illiquid market in such a way that very high liquidation costs are unlikely. To this end we introduce a discrete-time model that provides a simple device for designing and controlling the distribution of the revenues/costs from unwinding the position. By appealing to dynamic programming we derive semi-explicit formulas for the optimal execution strategies. We then present a numerical algorithm for approximating optimal execution rates as functions of the price. We provide error bounds and prove convergence. Finally, examples for the liquidation of forward positions in illiquid energy markets illustrate the efficiency of the algorithm.