This paper solves the dynamic investment problem of a risk averse manager compensated with a call option on the assets he controls. Under the manager's optimal policy, the option ends up either deep in or deep out of the money. Indivisible Timing Options, and Gambling, Operations Research, 61, 1, (126), (2013). To estimate the risk aversion coe cient with power utility using options and realized returns time series data, and test the logarithmic utility hypothesis (risk aversion equal to 1) at investment horizons spanning between 1 and 9 months. I fail to reject that the option implied risk aversion coe ecient is 1 at horizons between 3 and 9 months.

• Risk Aversion Indivisible Timing Options And Gambling System
• Risk Aversion Indivisible Timing Options And Gambling Disorder

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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.

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