Roadmap
The allocator line: probability, linear algebra, optimization, covariance estimation, constraints, and portfolio audit work.
The math a working quant actually uses — probability, differential equations, stochastic calculus, the Black–Scholes model, and numerical methods — built from the ground up with full derivations, worked examples, and graded problems.
The other half of quant math — vectors, matrices, eigenvalues, SVD, PCA, least-squares regression, and convex optimization — built to where you can extract PCA factors and solve a Markowitz portfolio by hand.
Probability made rigorous — sigma-algebras and measures, random variables as measurable maps, expectation as a Lebesgue integral, conditional expectation as an L^2 projection, and the limit theorems (LLN, CLT, extreme value) that underpin risk.
Build portfolios from expected returns, covariance estimates, constraints, transaction costs, and audit-ready risk evidence.
Regression through deep learning and transformers, applied to alpha discovery, credit risk, and backtest overfitting.
The frontier of derivatives valuation — backward SDEs and nonlinear Feynman–Kac, counterparty credit risk, the full XVA stack (CVA/DVA/FVA/KVA), and the Monte-Carlo and deep-BSDE methods that price them.
