Abstract

http://ssrn.com/abstract=1420239
 
 

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Noncommutative Geometry and Stochastic Calculus: Applications in Mathematical Finance


Eric A. Forgy


University of Illinois at Urbana-Champaign

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.

Number of Pages in PDF File: 15

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

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Date posted: June 16, 2009  

Suggested Citation

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

Contact Information

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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