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This research aims to formalize the Henstock-Kurzweil path integral for accurate pricing of European options under the Black-Scholes framework.

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 integrals for pricing European options, indicating robust mathematical foundations.

This research aims to formalize the Henstock-Kurzweil path integral for accurate pricing of European options under the Black-Scholes framework.
Developed a Gaussian-kernel Henstock-Kurzweil path integral for option pricing.
Provided a machine-checked formalization using Lean 4 / Mathlib.
Demonstrated the Chapman-Kolmogorov law and the closed-form price of a European call option.
Achieved a rigorous path-integral derivation of the European call price.
Confirmed the Gaussian kernel's role as a probability density.
Showed exactness of the drift-diffusion Chernoff splitting at every level for option pricing.

Berdinsky et al. (2026) studied this question.

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