Hedging in discrete time under transaction costs and continuous-time limit

Pierre F. Koehl, Huyên Pham, Nizar Touzi

Research output: Contribution to journalArticlepeer-review


We consider a discrete-time financial market model with L1 risky asset price process subject to proportional transaction costs. In this general setting, using a dual martingale representation we provide sufficient conditions for the super-replication cost to coincide with the replication cost. Next, we study the convergence problem in a stationary binomial model as the time step tends to zero, keeping the proportional transaction costs fixed. We derive lower and upper bounds for the limit of the super-replication cost. In the case of European call options and for a unit initial holding in the risky asset, the upper and lower bounds are equal. This result also holds for the replication cost of European call options. This is evidence (but not a proof) against the common opinion that the replication cost is infinite in a continuous-time model.

Original languageEnglish (US)
Pages (from-to)163-178
Number of pages16
JournalJournal of Applied Probability
Issue number1
StatePublished - Jan 1 1999


  • Continuous-time limit
  • Martingales
  • Replication
  • Super-replication
  • Transaction costs

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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