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2010•Theory of Probability and Mathematical StatisticsOpen access

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

Georgiy M. Shevchenko

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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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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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Available 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.

Key concepts: Arbitrage, Mathematics, Portfolio, Econometrics, Discrete time and continuous time, Financial market, Mathematical economics, Economics

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