Oct 2026· Zenodo (CERN European Organization for Nuclear Research)
Stochastic processes and financial applications
Abstract
A Lean 4 library of machine-checked mathematical-finance theorems: 535 sorry-free theorems, 522 of them delivery-ready, depending only on the axioms propext, Classical.choice and Quot.sound. It covers continuous-time stochastic calculus (the Ito integral, Ito's formula, quadratic variation and martingale representation), Black-Scholes pricing with the Greeks and exotics, jump-diffusion models (Merton's formula, Esscher pricing and variance swaps), binomial trees including the CRR-to-Black-Scholes limit and American options, the geometry of the American put exercise boundary, a polynomial-sign characterisation of raw SVI smiles whose call price is convex in the strike, fixed income, portfolio theory, coherent risk measures, quantitative risk management (value at risk for every loss law, expected shortfall for every integrable loss, copulas and extreme-value distributions), actuarial mathematics, market microstructure and DeFi. Built on Mathlib and Remy Degenne's BrownianMotion package. Every result is classified by how faithfully its Lean statement matches the mathematical claim, and a build-enforced axiom audit pins the axioms each proof depends on.
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