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Ural Mathematical Journal, 2016, Volume 2, Issue 2, Pages 37–44
DOI: https://doi.org/10.15826/umj.2016.2.004 (Mi umj19) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Group classification for a general nonlinear model of option pricing

Vladimir E. Fedorova, Mikhail M. Dyshaevb

a Laboratory of Quantum Topology, Mathematical Analysis Department, Chelyabinsk State University, Chelybinsk, Russia
b Mathematical Analysis Department, Chelyabinsk State University, Chekybinsk, Russia
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DOI: https://doi.org/10.15826/umj.2016.2.004
Abstract: We consider a family of equations with two free functional parameters containing the classical Black-Scholes model, Schonbucher-Wilmott model, Sircar-Papanicolaou equation for option pricing as partial cases. A five-dimensional group of equivalence transformations is calculated for that family. That group is applied to a search for specifications' parameters specifications corresponding to additional symmetries of the equation. Seven pairs of specifications are found.
Keywords: Nonlinear partial differential equation, Group analysis, Group of equivalency transformations, Group classiffcation, Nonlinear Black-Scholes equation, Pricing options, Dynamic hedging, Feedback effects of hedging.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.Z50.31.0020
The work is partially supported by Laboratory of Quantum Topology of Chelyabinsk State University (Russian Federation government grant 14.Z50.31.0020).
Bibliographic databases:
Document Type: Article
Language: English
Citation: Vladimir E. Fedorov, Mikhail M. Dyshaev, “Group classification for a general nonlinear model of option pricing”, Ural Math. J., 2:2 (2016), 37–44
Citation in format AMSBIB
\Bibitem{FedDys16}
\by Vladimir~E.~Fedorov, Mikhail~M.~Dyshaev
\paper Group classification for a general nonlinear model of option pricing
\jour Ural Math. J.
\yr 2016
\vol 2
\issue 2
\pages 37--44
\mathnet{http://mi.mathnet.ru/umj19}
\crossref{https://doi.org/10.15826/umj.2016.2.004}
\zmath{https://zbmath.org/?q=an:1398.91584}
\elib{https://elibrary.ru/item.asp?id=27447884}
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    • This publication is cited in the following 5 articles:
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