Symmetry analysis and exact solutions for a nonlinear model of the financial markets theory

Group classification is obtained for the Sircar-Papanicolaou equations family with a free parameter that contains the Black-Scholes equation as the simplest partial case. The five-dimensional group of equivalence transformations is calculated and three-dimensional kernel of principal Lie algebras and four-dimensional principal Lie algebras in cases of two free element specifications are found. Optimal subalgebras systems and corresponding invariant solutions or invariant submodels are calculated for every Lie algebra. Invariant solutions are included in more general multiparameter solutions families that are invariant with respect to the whole Lie algebra.