Skip to main content
Article thumbnail
Location of Repository

No arbitrage and closure results for trading cones with transaction costs

By Saul D. Jacka, Abdelkarem Berkaoui and Jon Warren


In this paper, we consider trading with proportional transaction costs as in Schachermayer’s paper (Schachermayer in Math. Finance 14:19–48, 2004). We give a necessary and sufficient condition for ${\mathcal{A}}$ , the cone of claims attainable from zero endowment, to be closed. Then we show how to define a revised set of trading prices in such a way that, firstly, the corresponding cone of claims attainable for zero endowment, ${\tilde{ {\mathcal{A}}}}$ , does obey the fundamental theorem of asset pricing and, secondly, if ${\tilde{ {\mathcal{A}}}}$ is arbitrage-free then it is the closure of ${\mathcal{A}}$ . We then conclude by showing how to represent claims

Topics: HB, QA
Publisher: Springer
Year: 2008
OAI identifier:

Suggested articles


  1. (1999). Coherent measures of risk, doi
  2. (2002). Coherent risk measures on general probability spaces." doi
  3. (2002). Hedging under transaction costs in currency markets: a discrete-time model. doi
  4. (2005). On low dimensional case in the fundamental asset pricing theorem with transaction costs. doi
  5. (1974). Measurable relations. doi
  6. (1998). Hedging and liquidation under transaction costs in currency markets, doi
  7. (2002). No-arbitrage criteria for markets with ecient friction,
  8. (2003). On the closedness of sums of convex cones in L0 and the robust no-arbitrage property, doi
  9. (1995). Arbitrage in securities markets with short-sales constraints. doi
  10. (1992). A Hilbert space proof of the fundamental theorem of asset pricing in discrete time. doi
  11. (2004). The fundamental theorem of asset pricing under proportional transaction costs in discrete time. doi
  12. (1990). Arbitrage et lois de martingale.
  13. (1970). Contribution a l'analyse convexe'. Thesis,
  14. (1971). Multiapplications mesurables a valeurs convexes compactes.
  15. (1980). Characterisation d'une classe d'ensembles convexes de L1 ou H1. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.