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Finance and Stochastics

, Volume 20, Issue 1, pp 99–121 | Cite as

Facelifting in utility maximization

  • Kasper Larsen
  • Halil Mete Soner
  • Gordan Žitković
Article

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 

Mathematics Subject Classification (2010)

91G10 91G80 60K35 

JEL Classification

C61 G11 

Notes

Acknowledgements

The authors would like to thank Mihai Sîrbu, Kim Weston, and the two anonymous referees for their many constructive comments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Kasper Larsen
    • 1
  • Halil Mete Soner
    • 2
  • Gordan Žitković
    • 3
  1. 1.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA
  2. 2.Department of MathematicsETHZürichSwitzerland
  3. 3.Department of MathematicsUniversity of Texas at AustinAustinUSA

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