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Ufa Mathematical Journal, 2017, Volume 9, Issue 1, Pages 29–40
DOI: https://doi.org/10.13108/2017-9-1-29 (Mi ufa363) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Symmetries and exact solutions of a nonlinear pricing options equation

M. M. Dyshaeva, V. E. Fedorovab

a Chelyabinsk State University, Br. Kashirinykh st. 129, 454001, Chelyabinsk, Russia
b South Ural State University (National Research University), Lenin av., 76, 454080, Chelyabinsk, Russia
English version PDF (371 kB) Citations (6)
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DOI: https://doi.org/10.13108/2017-9-1-29
Abstract: We study the group structure of the Schönbucher–Wilmott equation with a free parameter, which models the pricing options. We find a five-dimensional group of equivalence transformations for this equation. By means of this group we find four-dimensional Lie algebras of the admitted operators of the equation in the cases of two cases of the free term and we find a three-dimensional Lie algebra for other nonequivalent specifications. For each algebra we find optimal systems of subalgebras and the corresponding invariant solutions or invariant submodels.
Keywords: nonlinear partial differential equation, nonlinear Black–Scholes equation, Schönbucher–Wilmott model, pricing options, group analysis, invariant solution.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0011
1.6462.2017/БЧ
The work of the second author is supported by the Goverment of Russia (law no. 211, 16.03.2013), agreement no. 02.A03.21.0011 and by the Ministery of Education and Science of Russia, task no. 1.6462.2017/BCh).
Received: 28.12.2015
Russian version:
Ufimskii Matematicheskii Zhurnal, 2017, Volume 9, Issue 1, Pages 29–41
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 58J70, 76M60, 91G99, 35A30
Language: English
Original paper language: Russian
Citation: M. M. Dyshaev, V. E. Fedorov, “Symmetries and exact solutions of a nonlinear pricing options equation”, Ufimsk. Mat. Zh., 9:1 (2017), 29–41; Ufa Math. J., 9:1 (2017), 29–40
Citation in format AMSBIB
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\pages 29--41
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:126
    English version PDF:9
    References:29
     
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