Facelifting in utility maximization

© 2015, Springer-Verlag Berlin Heidelberg. 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

A simple characterization of tightness for convex solid sets of positive random variables

We show that for a convex solid set of positive random variables to be tight, or equivalently bounded in probability, it is necessary and sufficient to be radially bounded, i.e. that every ray passing through one of its elements eventually leaves the set. The result is motivated by problems arising in mathematical finance

Optimal consumption and investment under partial information

Portfolio optimization, Optimal consumption, Utility maximization, Partial Information, G11,