Facelifting in utility maximization

Kasper Larsen, Halil Mete Soner, Gordan Žitković

Research output: Contribution to journalArticle

3 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)99-121
Number of pages23
JournalFinance and Stochastics
Volume20
Issue number1
DOIs
StatePublished - Jan 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty

Keywords

  • Boundary layer
  • Convex analysis
  • Convex duality
  • Facelift
  • Financial mathematics
  • Incomplete markets
  • Markov processes
  • Unspanned endowment
  • Utility maximization

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