Merton portfolio optimization problem

Merton’s portfolio optimization problem is the choice an investor must make of how much of its wealth it should consume and how much it should allocate between stocks and a risk-free asset in order to maximize the expected utility. The focus of this work was to solve two of the cases of the Merton problem. For this, we studied some fundamental themes, such as: Dynamic Principle Programming (DPP) and the Hamilton-Jacobi-Bellmann Equation (HJB Equation). In addition, we review some concepts of Stochastic Processes and some important results of Itô Calculus. Merton’s portfolio optimization problem is well known in finance and the central ideas for solving it are adaptable to solving other finance problems.