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
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
Full-text PDF Free Access
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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.
References
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References
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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
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