e build on results of the section
( Change_of_measure_definition_section).
Suppose
that
is a numeraire with respect to the probability measure
and filtration
 .
By definitions, this means that for any traded asset
the ratio
is a
martingale:
and
 .
We will refer to the last positivity
condittion as the "suitable numeraire" condition. Suppose that
is a price of another acceptable
( )
instrument. We would like to produce a probability measure
so that for any traded asset
 
We
write 
Such transformation has the form
( Main property of change of
measure) with
 .
To determine the constant we recall that
 .
Hence, | | (Change of numeraire kernel) |
|
