Electronic Communications in Probability

Arbitrage-free Models In Markets With Transaction Costs

Hasanjan Sayit and Frederi Viens

Full-text: Open access


In the paper [7], Guasoni studies financial markets which are subject to proportional transaction costs. The standard martingale framework of stochastic finance is not applicable in these markets, since the transaction costs force trading strategies to have bounded variation, while continuous- time martingale strategies have infinite transaction cost. The main question that arises out of [7] is whether it is possible to give a convenient condition to guarantee that a trading strategy has no arbitrage. Such a condition was proposed and studied in [6] and [1], the so-called stickiness property, whereby an asset's price is never certain to exit a ball within a predetermined finite time. In this paper, we define the multidimensional extension of the stickiness property, to handle arbitrage-free conditions for markets with multiple assets and proportional transaction costs. We show that this condition is sufficient for a multi-asset model to be free of arbitrage. We also show that d-dimensional fractional Brownian models are jointly sticky, and we establish a time-change result for joint stickiness.

Article information

Electron. Commun. Probab., Volume 16 (2011), paper no. 53, 614-622.

Accepted: 4 July 2011
First available in Project Euclid: 7 June 2016

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 91G10: Portfolio theory
Secondary: 91B25: Asset pricing models 60G22: Fractional processes, including fractional Brownian motion

Financial markets arbitrage transaction cost sticky process fractional Brownian motion time-change

This work is licensed under aCreative Commons Attribution 3.0 License.


Sayit, Hasanjan; Viens, Frederi. Arbitrage-free Models In Markets With Transaction Costs. Electron. Commun. Probab. 16 (2011), paper no. 53, 614--622. doi:10.1214/ECP.v16-1671. https://projecteuclid.org/euclid.ecp/1465262009

Export citation


  • Bayraktar, Erhan; Sayit, Hasanjan. On the stickiness property. Quant. Finance 10 (2010), 1109-1112.
  • Cvitani'c, Jaksa; Karatzas, Ioannis. Hedging and portfolio optimization under transaction costs: a martingale approach. Math. Finance 6 (1996), 133-165.
  • Cheridito, Patrick. Arbitrage in fractional Brownian motion models. Finance Stoch 7 (2003), 533-553.
  • Cherny, Alexander. Brownian moving averages have conditional full support. Ann. Appl. Probab. 18 (2008), 1825-1830.
  • Guasoni, Paolo. No arbitrage under transaction costs, with fractional Brownian motion and beyond. Math. Finance 16 (2006), 569-582.
  • Guasoni, Paolo. Optimal investment with transaction costs and without semimartingales. Ann. Appl. Probab. 12 (2002), 1227-1246.
  • Guasoni, Paolo; R'asonyi, Mikl'os; Schachermayer, Walter. Consistent price systems and face-lifting pricing under transaction costs. Ann. Appl. Probab. 18 (2008), 491-520.
  • Karatzas, Ioannis; Shreve, Steven E.. Brownian motion and stochastic calculus. Springer-Verlag, New York, 1991.
  • Ha-Young Kim; Frederi Viens. Portfolio optimization with discrete proportional transaction costs under stochastic volatility. Accepted to Annals of Finance, 2010.
  • Protter, Philip E.. Stochastic integration and differential equations. Springer-Verlag, Berlin, 2005.
  • Rogers, L. C. G.. Arbitrage with fractional Brownian motion. Math. Finance 7 (1997), 95-105.
  • Sarol, Yalcin; Viens, Frederi G.; Zhang, Tao. Portfolio optimization with consumption in a fractional Black-Scholes market. Commun. Stoch. Anal. 1 (2007), 357-379.
  • Soner, H. M.; Shreve, S. E.; Cvitani'c, J. There is no nontrivial hedging portfolio for option pricing with transaction costs. Ann. Appl. Probab. 5 (1995), 327-355.
  • Touzi, Nizar. Super-replication under proportional transaction costs: from discrete to continuous-time models. Math. Methods Oper. Res. 50 (1999), 297-320.