Suppose an agent with positive wealth wishes to invest a proportion in a risky asset and the rest in a bond. The problem is to choose the optimal wealth percentage that maximizes your utility at the end of the investment period. This problem already has an analytical solution achieved by Merton in the 1960s and 1970s. The purpose of this work is to present numerical contributions in the approximation of the optimal portfolio that solves the Merton problem. To achieve this purpose, the following objectives are proposed: 1. Propose and compare a numerical scheme similar to the one presented by the author Kafash in his article Approximating the Solution of Stochastic Control Problems and the Merton's Portfolio Selection Model. 2. Present an algorithm based on neural networks that predicts the value of the optimal portfolio with simulated data. Due to the versatility of a neural network, this method is chosen for the prediction of optimal portfolios with empirical data, where its behavior and the subsequent correction through calibration are measured. This idea is left as work after what is presented here.
