Fractional Processes as Models in Stochastic Finance


We survey some new progress on the pricing models driven by fractional Brownian motion or mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We summarize some recent results on fractional Black & Scholes pricing model with transaction costs. We end the paper by giving some approximation results and indicating some open problems related to the paper.


Fractional Brownian motion Arbitrage Hedging in fractional models Approximation of geometric fractional Brownian motion 

Mathematics Subject Classification (2010)

91Gxx 91B70 60G15 60H05 



T.S. and E.V. acknowledge the support from Saarland University, and E.V. is grateful to the Academy of Finland, grant 127634, for partial support. We are grateful to Peter Parczewski and an anonymous referee for useful comments.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christian Bender
    • 1
  • Tommi Sottinen
    • 2
  • Esko Valkeila
    • 3
  1. 1.Department of MathematicsSaarland UniversitySaarbrückenGermany
  2. 2.Department of Mathematics and StatisticsUniversity of VaasaVaasaFinland
  3. 3.Department of Mathematics and Systems AnalysisAalto UniversityAaltoFinland

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