Article
Ufa Mathematical Journal
Volume 15, Number 4, pp. 112-125
On linear-autonomous symmetries of the fractional model of Guéant-Pu
Yadrikhinskiy Kh.V., Fedorov V.E.
DOI:10.13108/2023-15-4-112
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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.