This article is cited in 2 papers

Mathematics

Group analysis of a nonlinear generalization for Black — Scholes equation

M. M. Dyshaev

Chelyabinsk State University, Chelyabinsk, Russia

Abstract: Group classification is obtained for an equations family with a free parameter that contains Black — Scholes equation as a partial case. A five-dimensional group of equivalence transformations is calculated and three-dimensional principal Lie algebras in cases of two free element specifications were found. Optimal subalgebras systems and corresponding invariant solutions or invariant submodels are calculated for every Lie algebra.

Keywords: nonlinear partial differential equation, nonlinear Black — Scholes equation, Sircar — Papanicolaou equation, Schönbucher — Wilmott equation, group analysis, invariant solution, invariant submodel.

UDC: 517.957

Received: 26.09.2016
Revised: 03.10.2016

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