Paper: arXiv 2509.03916

Authors: Thibaut Mastrolia, Hao Wang

Abstract

We study the optimal liquidation problem in both lit and dark pools for investors facing execution uncertainty in a continuous-time setting with market impact. First, we design an optimal make–take fee policy for a large investor liquidating her position across both pools, interacting with small investors who pay trading fees. We explicitly characterize the large investor’s optimal liquidation strategies in both lit and dark pools using BSDEs under a compensation scheme proposed by an exchange to mitigate market impact in the lit venue. Second, we consider a purely competitive model with major–minor traders in the absence of regulation. We provide explicit solutions to the associated HJB–Fokker–Planck system. Finally, we illustrate our results through numerical experiments, comparing market impact under a regulated market with a strategic large investor to that in a purely competitive market with both small and large investors.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper exhibits high mathematical sophistication, utilizing stochastic control, BSDEs, Principal-Agent contract theory, and HJB-Fokker-Planck systems for optimal liquidation across lit and dark pools. However, its empirical validation relies on deep learning PDE solvers and numerical simulations rather than real-world market backtests or empirical transaction data.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Liquidation & Market Impact in Lit/Dark Pools] --> B[Model Framework & Inputs: Continuous-Time, Dark/Lit Venues, Make-Take Fees]
    B --> C[Scenario 1: Regulated Market<br/>Solve Large Investor Strategy via BSDEs]
    B --> D[Scenario 2: Competitive Market<br/>Solve Major-Minor System via HJB-Fokker-Planck]
    C --> E[Numerical Experiments & Simulation]
    D --> E
    E --> F[Outcomes: Characterized Optimal Execution Policies & Regulated vs. Competitive Impact Comparison]

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9 of 118 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.