Consistent price systems and face-lifting pricing under transaction costs

Paolo Guasoni, Mikloz Rasonyi, Walter Schachermayer

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

In markets with transaction costs, consistent price systems play the same role as martingale measures in frictionless markets. We prove that if a continuous price process has conditional full support, then it admits consistent price systems for arbitrarily small transaction costs. This result applies to a large class of Markovian and non-Markovian models, including geometric fractional Brownian motion.

Using the constructed price systems, we show, under very general assumptions, the following "face-lifting" result: the asymptotic superreplication price of a European contingent claim g(S-T) equals (g) over cap (S-0), where (g) over cap is the concave envelope of g and S-t is the price of the asset at time t. This theorem generalizes similar results obtained for diffusion processes to processes with conditional full support.

Original languageEnglish
Pages (from-to)491-520
Number of pages30
JournalAnnals of Applied Probability
Volume18
Issue number2
DOIs
Publication statusPublished - Apr 2008

Keywords / Materials (for Non-textual outputs)

  • transaction costs
  • superreplication
  • fractional Brownian motion
  • FRACTIONAL BROWNIAN-MOTION
  • SUPER-REPLICATION PROBLEM
  • FINITE DISCRETE-TIME
  • FUNDAMENTAL THEOREM
  • NO-ARBITRAGE
  • MARKETS
  • VERSION
  • MODEL

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