Optimal Trade Execution with a Dark Pool and Adverse Selection

Abstract

We consider the problem of optimally acquiring a position in a financial asset by submitting orders to a standard exchange and a dark pool. We assume that volatility is stochastic and trading at the standard exchange causes a price impact. Orders sent to the dark pool do not generate price impact. But they are not always filled and are exposed to adverse selection risk. Therefore, an optimal strategy has to find the right balance between favorable transaction prices and guaranteed execution. We consider two different optimality criteria: the expected implementation cost and an expected exponential of the implementation cost. In the first case, the optimal strategy can be given in closed form by a forward-backward system of stochastic equations. In the expected exponential case we characterize the optimal strategy by a Bellman equation that can be solved numerically.Our simulation experiments show that the presence of a dark pool lowers the average implementation cost and that the performance is improving if crossing probabilities in the dark pool increase.