In the seminal paper on optimal execution of portfolio transactions, Almgren and Chriss define 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. In this paper, we develop a model that accounts for volume uncertainty and show that a risk-averse trader has benefit in delaying their trades. We show that the optimal strategy is a trade-off between early and late trades to balance risk associated to both price and volume. With the incorporation of a risk term for the trade volume, the static optimal strategies obtained with our model avoid the explosion in the algorithmic complexity associated to dynamic programming solutions while yielding to competitive performance.
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