Portfolio liquidation under factor uncertainty

TL;DR

This paper investigates optimal asset liquidation strategies considering uncertainty in price impact parameters, revealing how ambiguity aversion influences trading behavior and costs through a semi-linear PDE framework.

Contribution

It introduces a novel model characterizing optimal liquidation under parameter ambiguity using a semi-linear PDE, and analyzes the impact of robustness on strategies and costs.

Findings

Ambiguity aversion increases liquidation rates.

Robust strategies are characterized by a semi-linear PDE.

Small uncertainty asymptotics show increased risk aversion effects.

Abstract

We study an optimal liquidation problem under the ambiguity with respect to price impact parameters. Our main results show that the value function and the optimal trading strategy can be characterized by the solution to a semi-linear PDE with superlinear gradient, monotone generator and singular terminal value. We also establish an asymptotic analysis of the robust model for small amount of uncertainty and analyse the effect of robustness on optimal trading strategies and liquidation costs. In particular, in our model ambiguity aversion is observationally equivalent to increased risk aversion. This suggests that ambiguity aversion increases liquidation rates.