Multi-Asset Liquidation in Dark Pools with Adverse Selection

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Highly relevant to quantitative trading, particularly for institutional traders executing large multi-asset portfolios through dark pools. The paper provides: (1) explicit optimal feedback strategies for simultaneous exchange and dark-pool execution; (2) quantitative insights into how adverse selection affects diversification benefits; (3) conditions under which cross-asset spillover can reverse the cost advantage of diversified portfolios; (4) shrinkage factors for dark-pool orders due to own-asset adverse selection; (5) conditions for diversification restoration via dark-pool execution. However, the reduced-form modeling of adverse selection and simplified execution mechanics limit direct implementation without calibration to real market data.

Extremely high complexity. The mathematical machinery involves matrix-valued BSDEs with Poisson jumps, singular terminal conditions, comparison principles in the Loewner order, and linearization techniques. Even the constant-coefficient reduction leads to a nonlinear matrix-valued Riccati ODE with singular terminal condition requiring careful numerical treatment (e.g., finite-terminal approximation with large L). The optimal feedback control involves matrix inversions (Σ⁻¹Y, N(Y)⁻¹M(Y)) that must be computed at each time step. The two-asset analysis requires solving coupled ODEs and tracking sign changes of state variables. Practical implementation would require significant numerical expertise and careful handling of the singularity near the terminal time.

The paper is purely theoretical with complete mathematical proofs. All results are self-contained with explicit assumptions (Assumption 3.1), theorem statements, and detailed proofs in Section 4. The two-asset numerical example (Figure 1) provides specific parameter values but no code repository is mentioned. Reproduction requires solving the singular matrix-valued Riccati ODE numerically (e.g., via finite-terminal approximation with L=1000 as stated). The mathematical framework is fully specified and verifiable by experts in BSDE theory.