Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 16 (2011), paper no. 53, 614-622.
Arbitrage-free Models In Markets With Transaction Costs
In the paper , 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  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  and , 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.
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
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