Multi-Asset Liquidation in Dark Pools with Adverse Selection
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摘要
This paper analyzes multi-asset portfolio liquidation in dark pools under quadratic adverse selection costs, formulating a multidimensional linear–quadratic stochastic control problem that leads to a matrix-valued BSDE with jumps and a singular terminal condition [page::1]. It establishes both existence and a novel uniqueness result for such matrix-valued BSDEs, a significant theoretical advancement even in simplified settings [page::2]. In a two-asset setting, the work reveals how asset correlation and spillover effects govern diversification: well-diversified portfolios can be protected if hedging dominates spillover, while adverse selection mainly determines whether a poorly diversified portfolio can be rescued via dark-pool trading [page::3]. The analysis hinges on a powerful comparison principle for multidimensional BSDEs with jumps and singular terminals, enabling the minimality argument and a rigorous uniqueness proof for the singular problem [page::4]. By contrasting with models without adverse selection, the paper shows how spillover reshapes diversification benefits and the role of dark pools in cross-asset liquidation, extending the dark-pool literature substantially [page::5].
