Geodesic
On linear-autonomous symmetries of Gu\'eant--Pu fractional model
Ufa mathematical journal, Tome 15 (2023) no. 4, pp. 112-125

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We study the group properties of the Guéant-Pu model with a fractional order in time, which describes the dynamics of option pricing. We find the groups of linear-autonomous equivalence transformations of the corresponding equation. With their help, we obtain a group classification of the fractional Guéant-Pu model with a nonlinear free element. In the case of a non-zero risk-free interest rate $r$, the underlying Lie algebra of such a model is one-dimensional. For zero $r$, the main Lie algebra is three-dimensional in the case of a special right-hand side and it is two-dimensional otherwise.
Keywords: Riemann-Liouville fractional derivative, fractional Guéant-Pu model, symmetry analysis, linear-autonomous transformation
Mots-clés : group of equivalence transformations, group classification. 
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     author = {Kh. V. Yadrikhinskiy and V. E. Fedorov},
     title = {On linear-autonomous symmetries of {Gu\'eant--Pu} fractional model},
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     publisher = {mathdoc},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2023_15_4_a7/}
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Kh. V. Yadrikhinskiy; V. E. Fedorov. On linear-autonomous symmetries of Gu\'eant--Pu fractional model. Ufa mathematical journal, Tome 15 (2023) no. 4, pp. 112-125. http://geodesic.mathdoc.fr/item/UFA_2023_15_4_a7/