Speaker: Kasper Larsen, Carnegie Mellon University
ABSTRACT
We establish the existence of and partially characterize a primal and dual facelift (discontinuity of the value function at the terminal time) for utility maximization in incomplete Markov-process driven financial markets. We deal with a general class of state-dependent utility functions and single out the concept of a ``subsistence cushion'' as central for the size of the facelift. Unlike in the pricing problems, and somewhat unexpectedly, facelifts exist in utility maximization despite strict convexity in the objective function. They show that the dual optimizer cannot be found in the set of countably-additive (martingale) measures in a wide variety situations and have important consequences for the development of numerical schemes for utility-maximization problems. Joint work with M. Soner and G. Zitkovic.