Investment Optimization with Nonlinear Equation Solving - Camilla, Aida Dwi; Febiyanti, Shintya Sukma; Rika Aprilia (Etunas, 2023)
Investment optimization is one of the important topics in the world of finance that aims to maximize profits with minimal risk. Mathematical approaches, particularly through the solution of nonlinear equations, have become an effective method of aiding investment decision-making. This article discusses the development of an investment optimization model that uses nonlinear equation solving techniques to determine optimal asset allocation. In this study, a nonlinear equation is used to describe the relationship between various investment variables, such as profit level, risk, and asset allocation. Using this approach, investors can find optimal solutions that meet their investment goals, whether in conservative, moderate, or aggressive scenarios. The methodology used involves historical data analysis, mathematical model formulation, and the application of numerical algorithms to solve the nonlinear equations. The results show that the solution of nonlinear equations is able to provide a more precise solution than traditional methods, such as linear programming or simple heuristic. This approach not only improves accuracy in determining the optimal portfolio, but also provides flexibility in dealing with dynamic market conditions. The proposed model allows sensitivity analysis to variable changes, allowing investors to make more informative and adaptive decisions. Investment optimization with the solution of nonlinear equations is a significant innovation in the field of finance, which not only supports investment efficiency but also opens up opportunities for the development of more complex investment models. This article is expected to be a reference for academics and practitioners in applying a mathematical approach for optimal portfolio management.