Title: Topology-Informed Approaches to Enhanced Index Tracking
Primary area: learning on time series and dynamical systems
Keywords: Topological Data Analysis, Time-series synthesis, Time-Series Featurization, Quantitative Finance, Mimicking Portfolio

Abstract: We address the problem of cross-market index tracking, replicating the performance of a foreign benchmark using only domestic assets, a task particularly relevant for markets with limited access to international investments. We propose a novel optimization framework that incorporates a topology-informed regularization term to extract persistent structural patterns from time-series price data. Our method leverages topological alignment between markets to construct robust index-mimicking portfolios without requiring constituent-level information. We further introduce a cost-aware formulation that accounts for transaction costs and their compounding effects. Empirical results on real-world data show notable gains over traditional tracking methods in both accuracy and robustness. Our approach holds broader potential for general time-series decomposition and synthesis.