On linear-autonomous symmetries of Guéant–Pu fractional model

Abstract

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.