Singular perturbation expansion for utility maximization with orderз- Quadratic transaction costs

Shiva Chandra, Andrew Papanicolaou

Research output: Contribution to journalArticle


We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order small, which leads to the optimization problem having an asymptotically-singular Hamilton-Jacobi-Bellman equation whose solution can be expanded in powers of . In this paper, we derive explicit formulae for the first two terms of this expansion. Analysis and simulation are provided to show the behavior of this approximating solution.

Original languageEnglish (US)
Article number1950039
JournalInternational Journal of Theoretical and Applied Finance
StateAccepted/In press - Jan 1 2019



  • aim portfolio
  • Merton problem
  • singular perturbation expansion
  • stochastic control
  • Transaction costs

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance(all)

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