Homogenization and Asymptotics for Small Transaction Costs: The Multidimensional Case

Dylan Possamaï, H. Mete Soner, Nizar Touzi

Research output: Contribution to journalArticlepeer-review


In the context of the multi-dimensional infinite horizon optimal consumption investment problem with small proportional transaction costs, we prove an asymptotic expansion. Similar to the one-dimensional derivation in our accompanying paper, the first order term is expressed in terms of a singular ergodic control problem. Our arguments are based on the theory of viscosity solutions and the techniques of homogenization which leads to a system of corrector equations. In contrast with the one-dimensional case, no explicit solution of the first corrector equation is available and we also prove the existence of a corrector and its properties. Finally, we provide some numerical results which illustrate the structure of the first order optimal controls.

Original languageEnglish (US)
Pages (from-to)2005-2046
Number of pages42
JournalCommunications in Partial Differential Equations
Issue number11
StatePublished - Nov 2 2015


  • Asymptotic expansions
  • Homogenization
  • Transaction costs
  • Viscosity solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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