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On the Approximation of Geometric Fractional Brownian Motion

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Optimality and Risk - Modern Trends in Mathematical Finance

Abstract

We give an approximation to geometric fractional Brownian motion. The approximation is a simple corollary to a ‘teletraffic’ functional central limit theorem by Gaigalas and Kaj in (Bernoulli 9:671–703, 2003). We analyze the central limit theorem of Gaigalas and Kaj from the point of view of semimartingale limit theorems to have a better understanding of the arbitrage in the limit model. With this approximation we associate the corresponding pricing model sequence, which has the no-arbitrage property and which is complete.

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Authors and Affiliations

  1. Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015, Helsinki, Finland

    Esko Valkeila

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  1. Esko Valkeila
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© 2009 Springer-Verlag Berlin Heidelberg

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Valkeila, E. (2009). On the Approximation of Geometric Fractional Brownian Motion. In: Optimality and Risk - Modern Trends in Mathematical Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02608-9_14

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