Group classification for a class of non-linear models of the RAPM type.

• Equivalence transformations are found for a class of Black–Scholes models. • The group classification for a class of nonlinear Black–Scholes models is obtained. • Multiparametric exact solutions for nonlinear Black–Scholes models are derived. A class of non-linear equations of RAPM (risk-adjusted pricing methodology) model type with a free element, depending on the second derivative with respect to the underlying asset, is studied. This class contains the Jandačka–Ševčovič model of the option pricing with taking into account transactions costs. The equivalence transformations continuous group of the equations class is found and is applied to the group classification obtaining for the model. The symmetries of the found free element specifications in the considered model are used for the deriving multi-parameter exact solutions. [ABSTRACT FROM AUTHOR]