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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2016, Volume 1, Issue 3, Pages 7–14 (Mi chfmj26)  
This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

Group analysis of a nonlinear generalization for Black — Scholes equation

M. M. Dyshaev

Chelyabinsk State University, Chelyabinsk, Russia
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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.
Received: 26.09.2016
Revised: 03.10.2016
Bibliographic databases:
Document Type: Article
UDC: 517.957
Language: Russian
Citation: M. M. Dyshaev, “Group analysis of a nonlinear generalization for Black — Scholes equation”, Chelyab. Fiz.-Mat. Zh., 1:3 (2016), 7–14
Citation in format AMSBIB
\Bibitem{Dys16}
\by M.~M.~Dyshaev
\paper Group analysis of a nonlinear generalization for Black~--- Scholes equation
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2016
\vol 1
\issue 3
\pages 7--14
\mathnet{http://mi.mathnet.ru/chfmj26}
\elib{https://elibrary.ru/item.asp?id=27541627}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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