Paper: arXiv 2405.14177
Authors: Xinman Cheng, Guanxing Fu, Xiaonyu Xia
Abstract
In this paper, we study the long time behavior of an optimal liquidation problem with semimartingale strategies and external flows. To investigate the limit rigorously, we study the convergence of three BSDEs characterizing the value function and the optimal strategy, from finite horizon to infinite horizon. We find that in the long time limit the player may not necessarily liquidate her assets at all due to the existence of external flows, even if in any given finite time horizon, the player is forced to liquidate all assets. Moreover, when the intensity of the external flow is damped, the player will liquidate her assets in the long run.
Complexity vs Empirical Score
- Math Complexity: 8.5/10
- Empirical Rigor: 1.5/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: This paper presents a rigorous theoretical study on optimal portfolio liquidation using backward stochastic differential equations (BSDEs) and semimartingale strategies. While mathematically sophisticated and novel in demonstrating non-liquidation limits under external flows, it lacks empirical backtesting or real-world data validation.
Research Flowchart
flowchart TD
A[Research Goal: Analyze long-time behavior of optimal liquidation with external flows] --> B[Data/Inputs: Semimartingale strategies, external flow intensities, execution costs]
B --> C[Methodology: Formulate 3 finite-horizon BSDEs for value function & strategy]
C --> D[Computational Process: Prove convergence of BSDEs from finite to infinite horizon]
D --> E[Outcome 1: Active External Flow<br>Player does NOT liquidate assets fully in infinite horizon]
D --> F[Outcome 2: Damped External Flow<br>Player fully liquidates assets in the long run]