Optimal Liquidation of an Asset under Drift Uncertainty
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 by allowing an arbitrary probability distribution to characterize 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 characterized as the unique solution to a nonlinear integral equation. We also study monotonicity properties with respect to the prior distribution and the asset volatility.
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Published In
SIAM Journal on Financial Mathematics
Pages: 357 - 381
DOI: 10.1137/15M1033265
ISSN (online): 1945-497X
Copyright
© 2016, Society for Industrial and Applied Mathematics.
History
Submitted: 31 July 2015
Accepted: 4 April 2016
Published online: 25 May 2016
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