Homogenization and asymptotics for small transaction costs

H. Mete Soner, Nizar Touzi

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


We consider the classical Merton problem of lifetime consumption-portfolio optimization with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic control problem which can be solved in closed form in the one-dimensional case. Unlike the existing literature, we consider a general utility function and general dynamics for the underlying assets. Our arguments are based on ideas from homogenization theory and use convergence tools from the theory of viscosity solutions. The multidimensional case is studied in our companion paper [D. Possamaï, H. M. Soner, and N. Touzi, Homogenization and Asymptotics for Small Transaction Costs: The Multidimensional Case, arXiv:1212.6275v2 [math.AP], preprint, 2012] using the same approach.

Original languageEnglish (US)
Pages (from-to)2893-2921
Number of pages29
JournalSIAM Journal on Control and Optimization
Issue number4
StatePublished - 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics


  • Asymptotic expansions
  • Homogenization
  • Transaction costs
  • Viscosity solutions


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