his section follows [Avellaneda1995].
Let
be a traded asset and the only state
variable:
under the risk neutral measure. We are considering a situation when the
analytical form of the function
is not known. However, we do assume
that
for all values of arguments. Following the conclusion
( Incomplete market ask) we are
seeking
for some final payoff function
 .
We introduce the
notation
for the value of the derivative
dependent on the particular assumption
about the volatility. For any
and all
we
have
The supremum is approached by some sequence
 .
Under sufficient regularity restrictions on the class of
we pass the above PDE to the
limit:
Clearly, the supremum is achieved
if 
Since the
is the only state variable, the delta hedging is performed in the regular way
using the
 .
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