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

Invariant Solutions and Conservation Laws of the Black-Scholes Equation

1
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, University of North-West, Mafikeng, Squth Africa
2
Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa
*
Authors to whom correspondence should be addressed.
Published: 1 April 2003
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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 Black-Scholes equation; optimal system; invariant solution
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Pooe, C.A.; Mahomed, F.M.; Soh, C.W. Invariant Solutions and Conservation Laws of the Black-Scholes Equation. Math. Comput. Appl. 2003, 8, 63-70.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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