The Feedback Effects in Illiquid Markets

The master thesis is devoted to an analysis of equilibrium or reaction-function models in illiquidity markets which was suggested by K. Ronnie Sircar and George Papanicolaou. The main equation is a nonlinear equation which is a perturbation of Black-Scholes model. By using Lie group analysis to determine the symmetry group of this equation. We present the Lie algebra of the Lie point transformations, the complete symmetry group and invariants. We use these invariants to reduce the PDE under investigation to ordinary differential equations (ODE). Solutions of these ODE's are subgroup-invariant solutions of the non-linear Black-Scholes equation. For some classes of those ODE's we find exact solutions and studied their properties.