A System of BSDEs with Singular Terminal Values Arising in Optimal Liquidation with Regime Switching

Paper: arXiv 2412.19058

Authors: Guanxing Fu, Xiaomin Shi, Zuo Quan Xu

Abstract

We study a stochastic control problem with regime switching arising in an optimal liquidation problem with dark pools and multiple regimes. The new feature of this model is that it introduces a system of BSDEs with jumps and with singular terminal values, which appears in literature for the first time. The existence result for this system is obtained. As a result, we solve the stochastic control problem with regime switching. More importantly, the uniqueness result of this system is also obtained, in contrast to merely minimal solutions established in most related literature.

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly sophisticated theoretical analysis of a system of coupled BSDEs with jumps and singular terminal values applied to optimal liquidation under regime switching. While mathematically rigorous and novel in its proof of uniqueness, it is entirely theoretical with no empirical backtests, simulations, or real market data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Liquidation with Dark Pools & Regime Switching] --> B[Inputs: Stochastic Market Parameters & Jump-Diffusion Regimes]
    B --> C[Methodology: Formulate Stochastic Control Problem]
    C --> D[Process: Derive System of BSDEs with Jumps & Singular Terminal Values]
    D --> E[Process: Prove Existence & Uniqueness of BSDE System Solution]
    E --> F[Outcomes: Complete Solution to Regime-Switching Optimal Liquidation]