Acta Applicandae Mathematicae

, Volume 138, Issue 1, pp 1–15 | Cite as

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

  • Martin Le Doux Mbele Bidima
  • Miklós Rásonyi


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.


Asymptotic exponential arbitrage Markov chains Large deviations Expected utility 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Martin Le Doux Mbele Bidima
    • 1
  • Miklós Rásonyi
    • 2
    • 3
  1. 1.University of Yaoundé IYaoundéCameroon
  2. 2.MTA Alfréd Rényi Institute of MathematicsBudapestHungary
  3. 3.University of EdinburghEdinburghUK

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