Mathematics for Trading

5 Core Chapters

Stochastic Calculus

Brownian motion, Itô’s lemma, SDEs, GBM, Heston model, jump-diffusion, numerical methods (Euler-Maruyama, Milstein). Monte Carlo in Rust with SIMD.

Market Microstructure

Limit Order Book anatomy, point processes (Poisson, Hawkes), Cont-Stoikov-Talreja model, Avellaneda-Stoikov optimal market making. Market making bot in Rust + WebSocket.

Portfolio Optimization

Mean-Variance (Markowitz), covariance shrinkage, Risk Parity, HRP, NCO. VaR, CVaR, Maximum Drawdown. Portfolio optimizer in Rust with convex solvers.

ML for Time Series

Feature engineering, LSTM, GRU, Transformer, TFT, volatility forecasting, Reinforcement Learning for trading. ONNX inference in Rust, RL trading agent.

Low Latency Systems

Ultra-low-latency architecture, memory management, lock-free data structures, TCP tuning, io_uring, CPU affinity, profiling. Production trading system in Rust.

Tech Stack

Every chapter includes production-ready code:

• Rust — primary implementation language, high-performance core
• Julia — research and rapid prototyping, SDE solvers
• Python — ML/DL workflows, PyTorch, scikit-learn, pandas

Prerequisites

• Calculus and linear algebra
• Probability theory basics
• Intermediate programming experience (any language)