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Invariant solutions of the Black-Scholes equation. (English) Zbl 1200.91309

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.

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
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