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Mathematics and Financial Economics

, Volume 1, Issue 3–4, pp 213–249 | Cite as

Asymptotic arbitrage and large deviations

  • H. Föllmer
  • W. Schachermayer
Article

Abstract

Typical models of mathematical finance admit equivalent martingale measures up to any finite time horizon but not globally, and this means that arbitrage opportunities arise in the long run. In this paper, we derive explicit estimates for asymptotic arbitrage, and we show how they are related to large deviation estimates for the market price of risk. As a case study we consider a geometric Ornstein–Uhlenbeck process. In this setting we also compute the optimal trading strategies and the resulting optimal growth rates of expected utility for all HARA utilities.

Keywords

Asymptotic arbitrage Utility maximization Large deviations Cost averaging 

JEL Classification

G11 G12 C61 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Vienna University of TechnologyWienAustria

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