A mean reversion selling rule with constraints

This paper is about an optimal asset-selling rule with trading constraints. The goal is to determine the time to sell the asset so a discounted reward function could be maximized. The underlying asset price evolves according to a mean-reverting model and the trading permission process is given in terms of a two-state {trading allowed, trading not allowed} Markov chain. It is shown that the optimal policy can be determined by a threshold level which can be obtained by solving the associated Hamilton-Jacobi-Bellman (HJB) equations (quasi-variational inequalities). A closed-form solution is obtained. A verification theorem is provided. Numerical experiments are also conducted to demonstrate the optimal policies and value functions.