e are facing evaluation of the expectation
under some probability measure and filtration
where the
and
are
adapted
processes. We are looking for a process
that would deliver the property
Hence, we would like to have
The last expression may be regarded as the formula
(
Main property of the change of
measure
)
with


(Common application of change of measure)

The normalization by
follows from the requirement
.
Note that such
is a martingale. In addition, the
must be positive. Thus, we also require that
would not change sign.
Another way to arrive to the same conclusion would be to
write
