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Path Integral Methods for Parabolic Partial Differential Equations with Examples from Computational Finance

Andrew Lyasoff
Organization: Boston University
Department: Department of Mathematics and Statistics
Journal / Anthology

The Mathematica Journal
Year: 2004
Volume: 9
Issue: 2
Page range: 299-422

By using specific examples--mostly from computational finance--this paper shows that Mathematica is capable of transforming Feynman-type integrals on the pathspace into powerful numerical procedures for solving general partial differential equations (PDEs) of parabolic type, with boundary conditions prescribed at some fixed or free time boundary. Compared to the widely used finite difference methods, such procedures are more universal, are considerably easier to implement, and do not require any manipulation of the PDE. An economist or a financial engineer who works with very general models for asset values, including the so-called stochastic volatility models, will find that this method is just as easy to work with as the classical Black-Scholes model, in which asset values can follow only a geometric Brownian motion process.

*Business and Economics
*Mathematics > Calculus and Analysis > Differential Equations

http://www.mathematica-journal.com/issue/v9i2/contents/ComputationalFinance/ComputationalFinance_1. [...]