Optimal Risk-Averse Timing of an Asset Sale: Trending vs Mean-Reverting Price Dynamics

Annals of Finance, Volume 15, Issue 1, pp.1–28, 2019

25 Pages Posted: 30 May 2016 Last revised: 12 Nov 2019

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Zheng Wang

Columbia University

Date Written: July 9, 2018

Abstract

This paper studies the optimal risk-averse timing to sell a risky asset. The investor’s risk preference is described by the exponential, power, or log utility. Two stochastic models are considered for the asset price – the geometric Brownian motion and exponential Ornstein-Uhlenbeck models – to account for, respectively, the trending and mean-reverting price dynamics. In all cases, we derive the optimal thresholds and certainty equivalents to sell the asset, and compare them across models and utilities, with emphasis on their dependence on asset price, risk aversion, and quantity. We find that the timing option may render the investor’s value function and certainty equivalent non-concave in price. Numerical results are provided to illustrate the investor’s strategies and the premium associated with optimally timing to sell.

Keywords: asset sale, risk aversion, certainty equivalent, optimal stopping, variational inequality

JEL Classification: C41, G11, G12

Suggested Citation

Leung, Tim and Wang, Zheng, Optimal Risk-Averse Timing of an Asset Sale: Trending vs Mean-Reverting Price Dynamics (July 9, 2018). Annals of Finance, Volume 15, Issue 1, pp.1–28, 2019, Available at SSRN: https://ssrn.com/abstract=2786176 or http://dx.doi.org/10.2139/ssrn.2786176

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

Zheng Wang

Columbia University ( email )

345 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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