Application of machine learning with asymptotic expansion to unconstrained optimal portfolio

This paper proposes a numerical method for solving unconstrained optimal portfolio problems. This method combines an asymptotic expansion method applied to the optimal portfolio problem in complete markets, a technique of reformulating the optimal portfolio problem into a corresponding backward stochastic differential equation (BSDE), and a method for BSDEs using machine learning. Numerical examples show that this method may give a better estimate for the optimal portfolio compared to existing methods.