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
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: Suggested Citation