Long Time Behavior of Optimal Liquidation Problems

TL;DR

This paper analyzes the long-term behavior of optimal asset liquidation strategies considering external flows, showing conditions under which assets are liquidated or retained over infinite time horizons.

Contribution

It introduces a rigorous analysis of the convergence of three BSDEs to understand long-term liquidation behavior with external flows.

Findings

External flows can prevent liquidation in the long run.

Damped external flows lead to asset liquidation over time.

Convergence of BSDEs characterizes the long-term strategy behavior.

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.