Noncommutative Geometry and Stochastic Calculus: Applications in Mathematical Finance

15 Pages Posted: 16 Jun 2009  

Eric A. Forgy

University of Illinois at Urbana-Champaign

Date Written: May 20, 2002

Abstract

The present report contains an introduction to some elementary concepts in noncommutative differential geometry. The material extends upon ideas first presented by Dimakis and Mueller-Hoissen. In particular, stochastic calculus and the Ito formula are shown to arise naturally from introducing noncommutativity of functions (0-forms) and differentials (1-forms). The abstract construction allows for the straightforward generalization to lattice theories for the direct implementation of numerical models. As an elementary demonstration of the formalism, the standard Black-Scholes model for option pricing is reformulated.

Keywords: Mathematical Finance, Black-Scholes Model, Stochastic Calculus, Noncommutative Geometry

Suggested Citation

Forgy, Eric A., Noncommutative Geometry and Stochastic Calculus: Applications in Mathematical Finance (May 20, 2002). Available at SSRN: https://ssrn.com/abstract=1420239 or http://dx.doi.org/10.2139/ssrn.1420239

Eric A. Forgy (Contact Author)

University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL 61820
United States

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