Topological Methods for Solving Nonlinear Equations in Financial Mathematics

Abstract

This paper explores the integration of topological methods in solving nonlinear equations within the realm of financial mathematics. It highlights the application of the Homotopy Analysis Method (HAM), Topological Degree Theory, and Iterative Methods derived from topological concepts, underscoring their theoretical foundations and practical implications. By applying these advanced mathematical techniques, the paper illustrates how complex financial models, especially those involving derivative pricing, risk management, and macroeconomic forecasting, can be effectively addressed. Theoretical formulations are accompanied by practical examples, demonstrating the utility and flexibility of topological methods in navigating the complexities of financial systems.