Stability of utility-maximization in incomplete markets

Kasper Larsen, Gordan Žitković

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


The effectiveness of utility-maximization techniques for portfolio management relies on our ability to estimate correctly the parameters of the dynamics of the underlying financial assets. In the setting of complete or incomplete financial markets, we investigate whether small perturbations of the market coefficient processes lead to small changes in the agent's optimal behavior, as derived from the solution of the related utility-maximization problems. Specifically, we identify the topologies on the parameter process space and the solution space under which utility-maximization is a continuous operation, and we provide a counterexample showing that our results are best possible, in a certain sense. A novel result about the structure of the solution of the utility-maximization problem, where prices are modeled by continuous semimartingales, is established as an offshoot of the proof of our central theorem.

Original languageEnglish (US)
Pages (from-to)1642-1662
Number of pages21
JournalStochastic Processes and their Applications
Issue number11
StatePublished - Nov 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


  • Appropriate topologies
  • Continuous semimartingales
  • Convex duality
  • Market price of risk process
  • Mathematical finance
  • Utility-maximization
  • V-relative compactness
  • Well-posedness


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