Skip to main content

Sticky Continuous Processes have Consistent Price Systems

  • Christian Bender (a1), Mikko S. Pakkanen (a2) and Hasanjan Sayit (a3)

Under proportional transaction costs, a price process is said to have a consistent price system, if there is a semimartingale with an equivalent martingale measure that evolves within the bid-ask spread. We show that a continuous, multi-asset price process has a consistent price system, under arbitrarily small proportional transaction costs, if it satisfies a natural multi-dimensional generalization of the stickiness condition introduced by Guasoni (2006).

Corresponding author
Postal address: Department of Mathematics, Saarland University, Postfach 151150, D-66041 Saarbrücken, Germany. Email address:
∗∗ Postal address: Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. Email address:
∗∗∗ Postal address: Department of Mathematical Sciences, Durham University, South Road, Durham DH1 3LE, UK. Email address:
Hide All
[1] Bayraktar, E. and Sayit, H. (2010). On the stickiness property. Quant. Finance 10, 11091112.
[2] Cherny, A. (2008). Brownian moving averages have conditional full support. Ann. Appl. Prob. 18, 18251830.
[3] Delbaen, F. and Schachermayer, W. (1994). “A general version of the fundamental theorem of asset pricing. Math. Ann. 300, 463520.
[4] Gasbarra, D., Sottinen, T. and van Zanten, H. (2011). Conditional full support of Gaussian processes with stationary increments. J. Appl. Prob. 48, 561568.
[5] Guasoni, P. (2006). No arbitrage under transaction costs, with fractional Brownian motion and beyond.” Math. Finance 16, 569582.
[6] Guasoni, P. and Rásonyi, M. (2015). Fragility of arbitrage and bubbles in local martingale diffusion models. Finance Stoch. 19, 215231.
[7] Guasoni, P., Rásonyi, M. and Schachermayer, W. (2008). Consistent price systems and face-lifting pricing under transaction costs.” Ann. Appl. Prob. 18, 491520.
[8] Guasoni, P., Rásonyi, M. and Schachermayer, W. (2010). The fundamental theorem of asset pricing for continuous processes under small transaction costs. Ann. Finance 6, 157191.
[9] Herczegh, A., Prokaj, V. and Rásonyi, M. (2014). Diversity and no arbitrage. Stoch. Anal. Appl. 32, 876888.
[10] Jouini, E. and Kallal, H. (1995). Martingales and arbitrage in securities markets with transaction costs. J. Econom. Theory 66, 178197.
[11] Kabanov, Y. and Stricker, C. (2008). On martingale selectors of cone-valued processes. In Séminaire de Probabilités XLI (Lecture Notes Math. 1934), Springer, Berlin, pp. 439442.
[12] Maris, F., Mbakop, E. and Sayit, H. (2011). “Consistent price systems for bounded processes. Commun. Stoch. Anal. 5, 633645.
[13] Pakkanen, M. S. (2010). Stochastic integrals and conditional full support. J. Appl. Prob. 47, 650667.
[14] Pakkanen, M. S. (2011). Brownian semistationary processes and conditional full support. Internat. J. Theoret. Appl. Finance 14, 579586.
[15] Revuz, D. and Yor, M. (1999). Continuous Martingales and Brownian Motion, 3rd edn. Springer, Berlin.
[16] Sayit, H. and Viens, F. (2011). Arbitrage-free models in markets with transaction costs. Electron. Commun. Prob. 16, 614622.
[17] Shiryaev, A. N. (1999). Essentials of Stochastic Finance: Facts, Models, Theory. World Scientific, River Edge, NJ.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


MSC classification