Topological Data Analysis for Economics and Finance: Mathematical Foundations, Algorithms, Applications

Topological Data Analysis for Economics and Finance introduces the mathematical ideas, computational methods and practical uses of topological data analysis for understanding complex economic and financial systems. It explains how the shape of data, including connected components, cycles and voids, can reveal fragmentation, feedback, contagion and structural change that averages, correlations and conventional models may overlook. The book develops the subject from set theory, linear algebra, real analysis and topology to simplicial complexes, homology, Betti numbers, persistent homology, persistence diagrams and the Mapper algorithm. It also presents algorithms, statistical inference, robustness testing and reproducible Python workflows. Applications cover digital-currency interoperability, financial-market instability, international trade networks, migration systems, banking crises and housing-market bubbles. Definitions, proofs, worked examples, exercises, solutions, code, notation tables and reporting guidance make the book a teaching resource and practical reference for students, researchers, analysts and policymakers.