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Facelifting in Utility Maximization

Author

Listed:
  • Kasper LARSEN

    (Carnegie Mellon University)

  • Mete SONER

    (ETH Zurich and Swiss Finance Institute)

  • Gordan ZITKOVIC

    (University of Texas)

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.

Suggested Citation

  • Kasper LARSEN & Mete SONER & Gordan ZITKOVIC, 2014. "Facelifting in Utility Maximization," Swiss Finance Institute Research Paper Series 14-61, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1461
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    File URL: http://ssrn.com/abstract=2512235
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    Cited by:

    1. Herdegen, Martin & Muhle-Karbe, Johannes, 2019. "Sensitivity of optimal consumption streams," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 1964-1992.

    More about this item

    Keywords

    Boundary layer; convex analysis; convex duality; facelift; financial mathematics; incomplete markets; Markov processes; utility-maximization; unspanned endowment;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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