Asset liquidation under drift uncertainty and regime-switching volatility

TL;DR

This paper develops a framework for optimal asset liquidation considering uncertain drift and regime-switching volatility, using filtering theory and optimal stopping to derive strategies and analyze structural properties.

Contribution

It introduces a novel approach combining filtering and optimal stopping for assets with unknown drift and Markov-switching volatility, extending analysis to general priors.

Findings

Derived an equivalent four-dimensional optimal stopping problem.

Constructed approximating sequences for analysis.

Provided detailed analysis for the two-point prior case.

Abstract

Optimal liquidation of an asset with unknown constant drift and stochastic regime-switching volatility is studied. The uncertainty about the drift is represented by an arbitrary probability distribution; the stochastic volatility is modelled by $m$-state Markov chain. Using filtering theory, an equivalent reformulation of the original problem as a four-dimensional optimal stopping problem is found and then analysed by constructing approximating sequences of three-dimensional optimal stopping problems. An optimal liquidation strategy and various structural properties of the problem are determined. Analysis of the two-point prior case is presented in detail, building on which, an outline of the extension to the general prior case is given.