  Kramkov and Sirbu (2006, 2007) have shown that first-order approximations of
power utility-based prices and hedging strategies can be computed by solving a
mean-variance hedging problem under a specific equivalent martingale measure
and relative to a suitable numeraire. In order to avoid the introduction of an
additional state variable necessitated by the change of numeraire, we propose
an alternative representation in terms of the original numeraire. More
specifically, we characterize the relevant quantities using semimartingale
characteristics similarly as in Cerny and Kallsen (2007) for mean-variance
hedging. These results are illustrated by applying them to exponential L\'evy
processes and stochastic volatility models of Barndorff-Nielsen and Shephard
type.
