Mathematical Modeling

James H. Simons, PhD: Using Mathematics to Make Money ArXiv ID: ssrn-4668072 “View on arXiv” Authors: Unknown Abstract In September 2022, James Simons spoke with members of the Journal of Investment Consulting editorial board about how his experience as a mathematician prepared Keywords: Quantitative Investing, Asset Management, Mathematical Modeling, Hedge Funds Complexity vs Empirical Score Math Complexity: 6.0/10 Empirical Rigor: 3.0/10 Quadrant: Lab Rats Why: The paper discusses advanced mathematical concepts like Chern-Simons invariants but focuses on philosophical and strategic insights from James Simons’ career, lacking specific formulas, code, or empirical backtesting details. flowchart TD A["Research Goal: How does mathematics prepare for quantitative investing?"] --> B["Data/Inputs: Simons Interview Data"] B --> C["Methodology: Qualitative Content Analysis"] C --> D["Computational Process: Identify Key Mathematical Concepts"] D --> E["Computational Process: Map Concepts to Investment Strategies"] E --> F["Key Findings: 1. Pattern Recognition 2. Data Modeling 3. Algorithmic Optimization 4. Risk Management"]

Branched Signature Model ArXiv ID: 2511.00018 “View on arXiv” Authors: Munawar Ali, Qi Feng Abstract In this paper, we introduce the branched signature model, motivated by the branched rough path framework of [“Gubinelli, Journal of Differential Equations, 248(4), 2010”], which generalizes the classical geometric rough path. We establish a universal approximation theorem for the branched signature model and demonstrate that iterative compositions of lower-level signature maps can approximate higher-level signatures. Furthermore, building on the existence of the extension map proposed in [“Hairer-Kelly. Annales de l’Institue Henri Poincaré, Probabilités et Statistiques 51, no. 1 (2015)”], we show how to explicitly construct the extension of the original paths into higher-dimensional spaces via a map $Ψ$, so that the branched signature can be realized as the classical geometric signature of the extended path. This framework not only provides an efficient computational scheme for branched signatures but also opens new avenues for data-driven modeling and applications. ...