Electronic Communications in Probability

Arbitrage-free Models In Markets With Transaction Costs

Hasanjan Sayit and Frederi Viens

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465262009

Digital Object Identifier
doi:10.1214/ECP.v16-1671

Mathematical Reviews number (MathSciNet)
MR2846654

Zentralblatt MATH identifier
1247.91173

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

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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


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