Super-replication under proportional transaction costs: From discrete to continuous-time models

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In this paper, we study the problem of finding the minimal initial capital (i.e. super-replication value) needed in order to hedge (without risk) European contingent claims in a Markov setting under proportional transaction costs. The main result is that the cheapest (trivial) buy-and-hold strategy is optimal. Such a negative result has been derived previously in different contexts. First, we focus on discrete-time binomial models. We prove that the continuous-time limit of the super-replication value is the cost of the cheapest buy-and-hold strategy. Then, the result is proved in a multivariate continuous-time model with Brownian filtration. As a direct consequence, we obtain an explicit characterization of the hedging set, i.e. the set of all initial positions in the market assets from which the contingent claim can be hedged through some admissible portfolio strategy.

Original languageEnglish (US)
Pages (from-to)297-320
Number of pages24
JournalMathematical Methods of Operations Research
Issue number2
StatePublished - Oct 1999


  • Continuous-time limit
  • Dynamic programming
  • Hedging options
  • Transaction costs
  • Viscosity solutions

ASJC Scopus subject areas

  • Software
  • General Mathematics
  • Management Science and Operations Research


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