A Formally Verified Library of Mathematical Finance in Lean 4

Battle Count: 68

This paper is about formal verification of classical financial mathematics, not about developing trading strategies, predictive models, or quantitative trading algorithms. Its relevance to quantitative trading is indirect: it provides machine-verified foundations for pricing theory, risk measures, and portfolio optimization that could underpin verified trading infrastructure. However, it produces no new financial results, no predictive models, and no trading signals. The contribution is methodological and infrastructural.

Extremely high complexity: ~52,300 lines of Lean 4 code across ~250 modules, requiring deep expertise in both mathematical finance (stochastic calculus, measure theory, PDEs) and formal verification (type theory, proof assistants, Mathlib internals). The continuous Itô integral construction via π-λ density arguments and norm-preserving extensions, the Girsanov change of measure, and the faithfulness audit infrastructure represent significant formal engineering challenges. Requires Lean 4, Mathlib, and BrownianMotion package expertise.

Excellent reproducibility: GitHub repository provided (https://github.com/raphaelrrcoelho/formal-mathfin), pinned Lean v4.31.0, Mathlib commit fabf563a, BrownianMotion commit bdf5ea0c in lean-toolchain and lake-manifest.json, pinned Docker image (ghcr.io/raphaelrrcoelho/mathfin-verify) reproduces the full build, AxiomAudit.lean serves as machine-checked evidence of sorry-freeness and axiom purity, coverage_report tool generates faithfulness tiers.