Abstract

The optimal trading strategy of a mean-reverting security, which follows the Ornstein-Uhlenbeck process, is considered for investors facing the fixed transaction fee and the proportional transaction fee, which is proportional to the number of trading shares, and trading in finite time. The mean-reverting feature is applied in deriving partial differential equations with optimal trading boundaries from the value function. The optimal trading boundaries include optimal trading prices, optimal positions after trading. Analytical solutions for optimal trading problems are obtained by theoretical analysis of partial differential equations and the optimal trading strategy is obtained by computational analysis for the optimal boundary conditions. The optimal trading strategy includes several optimal trading prices and optimal positions.