Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model

This paper investigates a continuous-time mean-variance portfolio selection problem based on log-return model. The financial market is composed of one risk-free asset and multiple risky assets whose prices are modelled by geometric Brownian motions. We derive sufficient condition for open-loop equilibrium strategies via forward backward stochastic differential equations (FBSDEs). An strategy derived solving the system. To illustrate our result, we consider special case where interest rate process described Vasicek In this case, also closed-loop through dynamic programming approach.