Multi-Asset Liquidation in Dark Pools with Adverse Selection

2026-07-29

AI Summary

This study addresses the optimal liquidation strategy for multi-asset portfolios in dark pools under adverse selection—a problem not previously resolved in the literature. By formulating a multidimensional stochastic control model incorporating quadratic adverse selection costs, the authors derive a matrix-valued backward stochastic differential equation (BSDE) featuring jumps and singular terminal conditions. They establish, for the first time, existence and uniqueness of solutions to such BSDEs, a novel result even in simplified settings. Theoretical analysis reveals that asset correlation and adverse selection exert fundamentally distinct effects on portfolio protection mechanisms: highly diversified portfolios are primarily governed by order spillover effects from dark pools, whereas the profitability of trading less diversified portfolios in dark pools hinges critically on the severity of adverse selection.

Abstract

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.

Problem

• multi-asset liquidation
• dark pools
• adverse selection
• portfolio diversification
• stochastic control

Innovation

• multi-asset liquidation
• dark pools
• adverse selection
• matrix-valued BSDE
• stochastic control