Aplicação de otimização não-linear para a modelagem de uma carteira de investimentos

Abstract

This work aimed to build an investment portfolio formed by assets traded on the B3 (Brazilian Stock Exchange) for the year 2025, using as the main tool, Nonlinear Optimization and theories from the world of Economics, in particular Markowitz’s Modern Portfolio Theory. The mathematical modeling results in a nonlinear problem, requiring the use of Nonlinear Programming to optimize an investment portfolio, in which the solution to this problem is provided through the Gradient Method and Newton’s Method, with the aid of the free software GNU Octave, compatible with MATLAB. The assets included in the research refer to an analysis of their performance for the second half of 2024 and the first half of 2025, in which the ten best assets during this period were analyzed, and the five assets that had the best correlations were selected. The work was also complemented with concepts of Financial Mathematics and some Statistical Parameters.