There are wide application of TDA in finance, it’s a relatively new area, hence worth exploration.

Topology and Financial Stability:

The paper “Topological Analysis of the Eurozone Interbank Market” by Bardoscia et al. (2015) applies tools from algebraic topology to study the stability and structure of the Eurozone interbank market. They use persistent homology to detect topological features that could indicate systemic risk and vulnerabilities in the network of financial institutions.

Persistent Homology in Financial Networks:

In “Topological Data Analysis of Financial Time Series: Landscapes of Crashes” by Filipe et al. (2013), persistent homology is employed to analyze financial time series data. The study identifies topological features (such as loops and voids) that correspond to periods of market instability or crashes, providing a novel perspective on systemic risk assessment.

Machine Learning and Topological Data Analysis:

The paper “Topological Methods for the Analysis of High-Dimensional Data Sets and 3D Object Recognition” by Carlsson (2009) discusses the application of persistent homology in various domains, including finance. While not solely focused on finance, it demonstrates the potential of topological data analysis (TDA) techniques in extracting meaningful patterns from complex datasets.

Homology and Network Analysis in Finance:

“Network-based Analysis of Persistent Financial Distress” by Rikos et al. (2019) applies homological methods to analyze financial distress networks, identifying critical nodes and structural vulnerabilities that contribute to financial instability.

The research identifies specific nodes (financial entities) that are crucial for the stability of the financial system based on their network position and topological characteristics. Structural Vulnerabilities: Insights are provided into structural vulnerabilities within the network, such as the presence of tightly interconnected groups (communities) or the existence of persistent topological features (loops, holes) that could amplify the impact of financial distress.

Topological Data Analysis in Economics:

In “Topological Data Analysis: A promising new field with application to economics” by Stoffelen and van der Leij (2018), the authors explore how TDA, including persistent homology, can be applied to economic datasets to uncover hidden structures and relationships that traditional methods might miss.