Geodesic
Symmetries and exact solutions of a~nonlinear pricing options equation
Ufa mathematical journal, Tome 9 (2017) no. 1, pp. 29-40

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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
Mots-clés : invariant solution. 
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M. M. Dyshaev; V. E. Fedorov. Symmetries and exact solutions of a~nonlinear pricing options equation. Ufa mathematical journal, Tome 9 (2017) no. 1, pp. 29-40. http://geodesic.mathdoc.fr/item/UFA_2017_9_1_a2/