AI 中文总结
本文针对暗池中带二次逆向选择成本的多资产清算问题，通过多维随机控制分析得出带跳奇异终端矩阵值BSDE，证明其解的存在性与唯一性，还揭示了资产相关性与逆向选择对不同分散度投资组合的影响。
AI 中文摘要
存在逆向选择的暗池中多资产清算问题在现有文献中仍未得到解决。本文通过分析一个多维随机控制问题，研究了二次逆向选择成本下暗池中的多资产投资组合清算问题，该问题会导出一个带跳且具有奇异终端条件的矩阵值倒向随机微分方程（BSDE）。除了建立解的存在性之外，我们的核心贡献在于证明了解的唯一性，这一结果即使在简化场景中也是新颖的，并强化了现有文献中的相关结论。在双资产情形下，我们进一步考察了资产相关性与逆向选择之间的相互作用：一方面，我们发现良好分散化投资组合的保护并非由逆向选择决定，而是由暗池订单的溢出效应决定；另一方面，我们表明逆向选择的主要作用是决定分散化程度差的投资组合能否通过暗池交易得到挽救。
英文摘要
We study the optimal liquidation of a multi-asset portfolio using both a traditional exchange and dark pools in the presence of quadratic adverse-selection costs. The problem leads to a matrix-valued backward stochastic differential equation with jumps and a singular terminal condition. We establish existence and uniqueness of its solution and use it to characterize the value function and the optimal liquidation strategy. The uniqueness result is the main mathematical contribution and strengthens the existing theory even in simpler special cases; the existence result is also new. For a two-asset model, we distinguish the roles of asset correlation, own-asset adverse selection, and cross-asset spillover in adverse-selection costs. Under diagonal temporary impact and in the absence of cross-asset spillover, an initially well-diversified portfolio remains well diversified during optimal liquidation and, for a fixed sign of the correlation, its liquidation cost is strictly decreasing in the magnitude of the correlation. By contrast, under the same diagonal-impact specification, under explicit conditions and sufficiently close to the liquidation horizon, cross-asset spillover makes a well-diversified portfolio more costly to liquidate than its poorly diversified sign-reversed counterpart and causes sufficiently unbalanced well-diversified portfolios to become poorly diversified with positive probability. Separately, without requiring diagonal temporary impact, we show that, in the absence of cross-asset spillover, own-asset adverse selection introduces an explicit shrinkage factor in the optimal dark-pool order relative to the order minimizing the post-execution continuation value. Finally, we derive an explicit condition under which a dark-pool execution transforms a poorly diversified portfolio into a well-diversified one.
Comments39 pages
