Invariant Solutions and Conservation Laws of the Black-Scholes Equation

C. A. Pooe; F. M. Mahomed; C. Wafo Soh

doi:10.3390/mca8010063

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Article

1 April 2003

Invariant Solutions and Conservation Laws of the Black-Scholes Equation

and

International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, University of North-West, Mafikeng, Squth Africa

Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa

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Math. Comput. Appl.2003, 8(1), 63-70;https://doi.org/10.3390/mca8010063

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Abstract

As the Black-Scholes equation can be transformed into the one-dimensional linear heat equation via two sets of transformations, an optimal system of one-dimensional subalgebras for the one-dimensional heat equation is exploited to obtain two classes of optimal systems of one-dimensional subalgebras for the well-known Black-Scholes equation of the mathematics of finance. Two methods for the derivation of the two classes of optimal systems of group-invariant solutions for this model are available. We present the simpler approach

Keywords:

Black-Scholes equation; optimal system; invariant solution

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