  In this paper we consider the problem of the quantile hedging from the point
of view of a better informed agent acting on the market. The additional
knowledge of the agent is modelled by a filtration initially enlarged by some
random variable. By using equivalent martingale measures introduced in
Amendinger (2000) and Amendinger, Imkeller and Schweizer (1998) we solve the
problem for the complete case, by extending the results obtained in F{\"o}llmer
and Leukert (1999) to the insider context. Finally, we consider the examples
with the explicit calculations within the standard Black-Scholes model.
