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This work aims to apply the Henstock-Kurzweil path integral to establish a machine-verified approach to pricing European options.

July 28, 2026Open Access

Henstock–Kurzweil Path Integral in Financial Mathematics: A Machine-Verified Pricing of European and Barrier Options

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Randomized trial applies Henstock-Kurzweil path-integral to European option pricing, suggesting robust mathematical formalization.

This work aims to apply the Henstock-Kurzweil path integral to establish a machine-verified approach to pricing European options.
Utilized the Gaussian-kernel Henstock-Kurzweil path-integral machinery in a novel financial context.
Formalized the process using Lean 4 / Mathlib, ensuring all results are rigorously checked.
Derived the closed-form price of a European call option directly from the Gaussian kernel and proved various mathematical properties.
Successfully obtained the Black-Scholes formula for European call options as C = S_0 N(d₁) − K e^(−rT) N(d₂).
Demonstrated that the transition density functions adhere to the Chapman-Kolmogorov law and possess strong continuity.
Confirmed that the drift-diffusion Chernoff splitting is exact at all levels, establishing a rigorous path-integral derivation.

Berdinsky et al. (2026) studied this question.

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