Two expository reference documents connecting the mathematical foundations of common financial models to the supervisory frameworks that govern them.
1. From Mathematical Foundations to Regulatory Practice A domain-focused piece mapping four foundational techniques — stochastic calculus, non-convex optimization, Fourier analysis, and wavelet transforms — to where each appears in derivatives valuation, model validation, ML development, and time-series analysis, with notes connecting them to current model-risk and AI-governance frameworks (SR 26-2, NIST AI RMF, the EU AI Act).
2. Foundations of Mathematical Analysis A self-contained companion treatment with complete, step-by-step proofs of the underlying results (Fourier convergence and the Gibbs phenomenon, the Itô integral, non-convex optimization, and the Haar wavelet system).
These are intended to demonstrate applied understanding across the model-risk and AI-governance domain — the ability to connect quantitative fundamentals to practical governance and validation work. They are expository: the results are classical and well-established, and the contribution is the synthesis and the bridge between the mathematical and regulatory domains, not new research.
- Regulatory references are current as of June 2026; supervisory guidance and statutory timelines evolve, and citations should be re-verified against primary sources before reliance.
- The mathematical proofs are pending external review by qualified subject-matter experts; they are shared as a rigorous study-and-reference resource.
- This material is informational and is not legal, regulatory, or investment advice.