Multi-Asset Liquidation in Dark Pools with Adverse Selection

Multi-asset liquidation in dark pools with adverse selection remains unsolved in literature. In this paper, we investigate multi-asset portfolio liquidation in dark pools with quadratic adverse selection cost by analyzing a multidimensional stochastic control problem, which leads to a matrix-valued BSDE with jumps and a singular terminal condition. Beyond establishing the existence of a solution, our key contribution lies in proving uniqueness, a result that is novel even in simplified settings and strengthens existing findings in the literature. In the two-asset case, we further examine the interaction between asset correlation and adverse selection. On the one hand, we find that the protection of a well-diversified portfolio is not determined by adverse selection but rather by the spillover effects of dark-pool orders. On the other hand, we show that the primary role of adverse selection is to determine whether a poorly diversified portfolio can be rescued through dark-pool trading.