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Finance and Stochastics

, Volume 8, Issue 2, pp 181–206 | Cite as

Asymptotic analysis for optimal investment and consumption with transaction costs

  • Karel Janeček
  • Steven E. Shreve
Article

Abstract.

We consider an agent who invests in a stock and a money market and consumes in order to maximize the utility of consumption over an infinite planning horizon in the presence of a proportional transaction cost \(\lambda > 0\). The utility function is of the form U(c) = c 1-p /(1-p) for p > 0, \(p\neq 1\). We provide a heuristic and a rigorous derivation of the asymptotic expansion of the value function in powers of \(\lambda^{1/3}\), and we also obtain asymptotic results on the boundary of the “no-trade” region.

Keywords:

Transaction costs optimal control asymptotic analysis utility maximation 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Department of Mathematical Sciences and Center for Computational FinanceCarnegie Mellon UniversityPittsburghUSA

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