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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
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.
Received: 28.12.2015
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
Linking options:
https://www.mathnet.ru/eng/ufa363https://doi.org/10.13108/2017-9-1-29 https://www.mathnet.ru/eng/ufa/v9/i1/p29
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Abstract page: | 2480 | Russian version PDF: | 126 | English version PDF: | 9 | References: | 29 |
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