Pooe, C. A.; Mahomed, F. M.; Wafo Soh, C. Invariant solutions of the Black-Scholes equation. (English) Zbl 1200.91309 Math. Comput. Appl. 8, No. 1, 63-70 (2003). Summary: 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. Cited in 2 Documents MSC: 91G80 Financial applications of other theories 35A30 Geometric theory, characteristics, transformations in context of PDEs 35Q91 PDEs in connection with game theory, economics, social and behavioral sciences 91G10 Portfolio theory PDF BibTeX XML Cite \textit{C. A. Pooe} et al., Math. Comput. Appl. 8, No. 1, 63--70 (2003; Zbl 1200.91309) Full Text: DOI OpenURL