  We study a financial model with a non-trivial price impact effect. In this
model we consider the interaction of a large investor trading in an illiquid
security, and a market maker who is quoting prices for this security. We assume
that the market maker quotes the prices such that by taking the other side of
the investor's demand, the market maker will arrive at maturity with maximal
expected wealth. Within this model we concentrate on the issue of contingent
claims' hedging.
