Optimal liquidation of an asset under drift uncertainty

TL;DR

This paper develops an optimal stopping strategy for asset liquidation under drift uncertainty, using Bayesian filtering and characterizing the stopping time through a non-linear integral equation.

Contribution

It introduces a Bayesian framework for asset liquidation with unknown drift, deriving a stopping rule based on posterior mean dynamics and integral equations.

Findings

Optimal stopping time as first passage of posterior mean

Characterization of the boundary via non-linear integral equation

Monotonicity properties with respect to prior and volatility

Abstract

We study a problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. Taking a Bayesian approach, we model the initial beliefs of an individual about the drift parameter by allowing an arbitrary probability distribution to characterise the uncertainty about the drift parameter. Filtering theory is used to describe the evolution of the posterior beliefs about the drift once the price process is being observed. An optimal stopping time is determined as the first passage time of the posterior mean below a monotone boundary, which can be characterised as the unique solution to a non-linear integral equation. We also study monotonicity properties with respect to the prior distribution and the asset volatility.