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Theory of Probability and Mathematical Statistics

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Arbitrage in a discrete time model of a financial market with a taxation proportional to the portfolio size


Author: G. M. Shevchenko
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 81 (2010).
Journal: Theor. Probability and Math. Statist. 81 (2010), 177-186
MSC (2010): Primary 91B30
DOI: https://doi.org/10.1090/S0094-9000-2011-00818-6
Published electronically: January 20, 2011
MathSciNet review: 2667318
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Abstract: We introduce the notion of $ V^\varepsilon$-arbitrage (in other words, an arbitrage under the taxation proportional to the portfolio size) for a multiperiod discrete time model of a financial market. For a $ V^\varepsilon$-arbitrage, we prove a result analogous to the classical fundamental asset pricing theorem. Differences between a $ V^\varepsilon$-arbitrage and some other notions of arbitrage are analyzed.


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Additional Information

G. M. Shevchenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: zhora@univ.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-2011-00818-6
Keywords: Arbitrage, transaction costs, portfolio size constraints, martingale measure, measurable choice theorem
Received by editor(s): September 28, 2009
Published electronically: January 20, 2011
Article copyright: © Copyright 2011 American Mathematical Society

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