Portfolio Liquidation and Ambiguity Aversion

We consider an optimal execution problem where an agent holds a position in an asset which must be liquidated (using limit orders) before a terminal horizon. Beginning with a standard model for the trading dynamics, we analyse how the acknowledgement of model misspecification affects the agent's optimal trading strategy. The three possible sources of misspecification in this context are: (i) the arrival rate of market orders, (ii) the fill probability of limit orders, and (iii) the dynamics of the asset price. We show that ambiguity aversion with respect to each factor of the model has a similar effect on the optimal strategy, but the magnitude of the effect depends on time and inventory position in different ways depending on the source of uncertainty. In addition we allow the agent to employ market orders to further increase the strategy's profitability and show the effect of ambiguity aversion on the shape of the optimal impulse region. In some cases we have a closed-form expression for the optimal trading strategy which significantly enhances the efficiency in which the strategy can be executed in real time