  We establish the existence and characterization of a primal and a dual
facelift - discontinuity of the value function at the terminal time - for
utility-maximization in incomplete semimartingale-driven financial markets.
Unlike in the lower- and upper-hedging problems, and somewhat unexpectedly, a
facelift turns out to exist in utility-maximization despite strict convexity in
the objective function. In addition to discussing our results in their natural,
Markovian environment, we also use them to show that the dual optimizer cannot
be found in the set of countably-additive (martingale) measures in a wide
variety of situations.
