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Fractional Processes as Models in Stochastic Finance

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Advanced Mathematical Methods for Finance

Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematics, Saarland University, P.O. Box 151150, 66041, Saarbrücken, Germany

    Christian Bender

  2. Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, 65101, Vaasa, Finland

    Tommi Sottinen

  3. Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, 00076, Aalto, Finland

    Esko Valkeila

Authors
  1. Christian Bender
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  2. Tommi Sottinen
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  3. Esko Valkeila
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Correspondence to Esko Valkeila .

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Editors and Affiliations

  1. CMA, Department of Mathematics, University of Oslo, Oslo, 0316, Norway

    Giulia Di Nunno

  2. CMA, Department of Mathematics, University of Oslo, Oslo, 0316, Norway

    Bernt Øksendal

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Bender, C., Sottinen, T., Valkeila, E. (2011). Fractional Processes as Models in Stochastic Finance. In: Di Nunno, G., Øksendal, B. (eds) Advanced Mathematical Methods for Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18412-3_3

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