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2011 Arbitrage-free Models In Markets With Transaction Costs
Hasanjan Sayit, Frederi Viens
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Electron. Commun. Probab. 16: 614-622 (2011). DOI: 10.1214/ECP.v16-1671


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.


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Hasanjan Sayit. Frederi Viens. "Arbitrage-free Models In Markets With Transaction Costs." Electron. Commun. Probab. 16 614 - 622, 2011.


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

zbMATH: 1247.91173
MathSciNet: MR2846654
Digital Object Identifier: 10.1214/ECP.v16-1671

Primary: 91G10
Secondary: 60G22 , 91B25

Keywords: Arbitrage , Financial markets , fractional Brownian motion , sticky process , time-change , transaction cost


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