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

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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 (Mbele Bidima and Rásonyi in Ann. Oper. Res. 200:131–146, 2012), 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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Notes

  1. This is not a restriction of generality. If we had \(\mathbb{E}\varepsilon_{1}=m\), we could replace μ(x) by μ′(x):=μ(x)+σ(x)m and ε t by \(\varepsilon_{t}':=\varepsilon_{t}-m\) and in this way get back to the case \(\mathbb{E}\varepsilon_{1}=0\).

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Authors and Affiliations

  1. University of Yaoundé I, Yaoundé, Cameroon

    Martin Le Doux Mbele Bidima

  2. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Miklós Rásonyi

  3. University of Edinburgh, Edinburgh, UK

    Miklós Rásonyi

Authors
  1. Martin Le Doux Mbele Bidima
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  2. Miklós Rásonyi
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Correspondence to Miklós Rásonyi.

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The authors thank the referee and the associate editor for extremely constructive and helpful reports.

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Mbele Bidima, M.L.D., Rásonyi, M. Asymptotic Exponential Arbitrage and Utility-Based Asymptotic Arbitrage in Markovian Models of Financial Markets. Acta Appl Math 138, 1–15 (2015). https://doi.org/10.1007/s10440-014-9955-3

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  • DOI: https://doi.org/10.1007/s10440-014-9955-3

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