  The studied model was suggested to design a perfect hedging strategy for a
large trader. In this case the implementation of a hedging strategy affects the
price of the underlying security. The feedback-effect leads to a nonlinear
version of the Black-Scholes partial differential equation. Using the Lie group
theory we reduce the partial differential equation in special cases to ordinary
differential equations. The found Lie group of the model equation gives rise to
invariant solutions. Families of exact invariant solutions for special values
of parameters are described.
