Facelifting in Utility Maximization

26 Pages Posted: 21 Oct 2014

See all articles by Kasper Larsen

Kasper Larsen

Rutgers, The State University of New Jersey

Halil Mete Soner

ETH Zürich; Swiss Finance Institute

Gordan Zitkovic

University of Texas at Austin

Date Written: October 20, 2014

Abstract

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

Larsen, Kasper and Soner, Halil Mete and Zitkovic, Gordan, Facelifting in Utility Maximization (October 20, 2014). Swiss Finance Institute Research Paper No. 14-61, Available at SSRN: https://ssrn.com/abstract=2512235 or http://dx.doi.org/10.2139/ssrn.2512235

Kasper Larsen

Rutgers, The State University of New Jersey ( email )

311 North 5th Street
New Brunswick, NJ 08854
United States

Halil Mete Soner (Contact Author)

ETH Zürich ( email )

Zürichbergstrasse 18
8092 Zurich, CH-1015
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Gordan Zitkovic

University of Texas at Austin ( email )

2317 Speedway
Austin, TX 78712
United States

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