Optimal execution strategy with an uncertain volume target

In a seminal 2001 paper on the optimal execution of portfolio transactions, Almgren and Chriss defined the optimal trading strategy to liquidate a fixed volume of a single security under price uncertainty. Yet there exist situations, such as in the power market, in which the volume to be traded can only be estimated and becomes more accurate when approaching a specified delivery time. During the course of execution a trader should then constantly adapt their trading strategy to meet their fluctuating volume target. In this paper we develop a model that accounts for volume uncertainty and we show that a risk-averse trader benefits from delaying their trades. More precisely, we argue that the optimal strategy is a trade-off between early and late trades in order to balance risk that is associated with both price and volume. By incorporating a risk term related to the trading volume, the static optimal strategies that are suggested by our model avoid the blowup in the algorithmic complexity usually associated with dynamic programming solutions while yielding competitive performance.