  We study the sensitivity of the expected utility maximization problem in a
continuous semi-martingale market with respect to small changes in the market
price of risk. Assuming that the preferences of a rational economic agent are
modeled with a general utility function, we obtain a second-order expansion of
the value function, a first-order approximation of the terminal wealth, and
construct trading strategies that match the indirect utility function up to the
second order. If a risk-tolerance wealth process exists, using it as a
num\'eraire and under an appropriate change of measure, we reduce the
approximation problem to a Kunita-Watanabe decomposition.
