No Arbitrage Under Transaction Costs, with Fractional Brownian Motion and Beyond

14 Pages Posted: 12 Jun 2006

See all articles by Paolo Guasoni

Paolo Guasoni

Boston University - Department of Mathematics and Statistics; Dublin City University - School of Mathematical Sciences; University of Bologna - Department of Statistics

Abstract

We establish a simple no-arbitrage criterion that reduces the absence of arbitrage opportunities under proportional transaction costs to the condition that the asset price process may move arbitrarily little over arbitrarily large time intervals.

We show that this criterion is satisfied when the return process is either a strong Markov process with regular points, or a continuous process with full support on the space of continuous functions. In particular, we prove that proportional transaction costs of any positive size eliminate arbitrage opportunities from geometric fractional Brownian motion for H E (0, 1) and with an arbitrary continuous deterministic drift.

Suggested Citation

Guasoni, Paolo and Guasoni, Paolo, No Arbitrage Under Transaction Costs, with Fractional Brownian Motion and Beyond. Mathematical Finance, Vol. 16, No. 3, pp. 569-582, July 2006, Available at SSRN: https://ssrn.com/abstract=907706 or http://dx.doi.org/10.1111/j.1467-9965.2006.00283.x

Paolo Guasoni (Contact Author)

Boston University - Department of Mathematics and Statistics ( email )

Boston, MA 02215
United States

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

HOME PAGE: http://www.guasoni.com

University of Bologna - Department of Statistics ( email )

Bologna, 40126
Italy

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