  As soon as one accepts to abandon the zero-risk paradigm of Black-Scholes,
very interesting issues concerning risk control arise because different
definitions of the risk become unequivalent. Optimal hedges then depend on the
quantity one wishes to minimize. We show that a definition of the risk more
sensitive to the extreme events generically leads to a decrease both of the
probability of extreme losses and of the sensitivity of the hedge on the price
of the underlying (the `Gamma'). Therefore, the transaction costs and the
impact of hedging on the price dynamics of the underlying are reduced.
