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.
Math. Comput. Appl. 2003, 8(1), 63-70; https://doi.org/10.3390/mca8010063
Published: 1 April 2003
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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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. https://doi.org/10.3390/mca8010063
AMA Style
Pooe CA, Mahomed FM, Soh CW. Invariant Solutions and Conservation Laws of the Black-Scholes Equation. Mathematical and Computational Applications. 2003; 8(1):63-70. https://doi.org/10.3390/mca8010063
Chicago/Turabian StylePooe, C. A., F. M. Mahomed, and C. Wafo Soh. 2003. "Invariant Solutions and Conservation Laws of the Black-Scholes Equation" Mathematical and Computational Applications 8, no. 1: 63-70. https://doi.org/10.3390/mca8010063
