SINGULAR PERTURBATION EXPANSION for UTILITY MAXIMIZATION with ORDER-∈ QUADRATIC TRANSACTION COSTS

Shiva Chandra, Andrew Papanicolaou

Research output: Contribution to journalArticle

Abstract

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
Volume22
Issue number7
DOIs
StatePublished - Nov 1 2019

Keywords

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

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance(all)

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