Facelifting in Utility Maximization
26 Pages Posted: 21 Oct 2014
Date Written: October 20, 2014
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.
Keywords: Boundary layer, convex analysis, convex duality, facelift, financial mathematics, incomplete markets, Markov processes, utility-maximization, unspanned endowment.
JEL Classification: C61, G11.
Suggested Citation: Suggested Citation