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Asymptotic Exponential Arbitrage and Utility-based Asymptotic Arbitrage in Markovian Models of Financial Markets

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  • Martin Le Doux Mbele Bidima
  • Mikl'os R'asonyi

Abstract

Consider a discrete-time infinite horizon financial market model in which the logarithm of the stock price is a time discretization of a stochastic differential equation. Under conditions different from those given in a previous paper of ours, we prove the existence of investment opportunities producing an exponentially growing profit with probability tending to $1$ geometrically fast. This is achieved using ergodic results on Markov chains and tools of large deviations theory. Furthermore, we discuss asymptotic arbitrage in the expected utility sense and its relationship to the first part of the paper.

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  • Martin Le Doux Mbele Bidima & Mikl'os R'asonyi, 2014. "Asymptotic Exponential Arbitrage and Utility-based Asymptotic Arbitrage in Markovian Models of Financial Markets," Papers 1406.5312, arXiv.org.
    • Handle: RePEc:arx:papers:1406.5312
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    References listed on IDEAS

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    1. Martin Mbele Bidima & Miklos Rasonyi, 2012. "On long-term arbitrage opportunities in Markovian models of financial markets," Annals of Operations Research, Springer, vol. 200(1), pages 131-146, November.
    2. Nikolai Dokuchaev, 2007. "Mean-Reverting Market Model: Speculative Opportunities and Non-Arbitrage," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 319-337.
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