Acta Applicandae Mathematicae

, Volume 138, Issue 1, pp 1–15

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

Article

DOI: 10.1007/s10440-014-9955-3

Cite this article as:
Mbele Bidima, M.L.D. & Rásonyi, M. Acta Appl Math (2015) 138: 1. doi:10.1007/s10440-014-9955-3

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.

Keywords

Asymptotic exponential arbitrage Markov chains Large deviations Expected utility 

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

Personalised recommendations