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Donsker theorem for the Rosenblatt process and a binary market model

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  • Ciprian Tudor

    (CES, SAMOS)

  • Soledad Torres

Abstract

In this paper, we prove a Donsker type approximation theorem for the Rosenblatt process, which is a selfsimilar stochastic process exhibiting long range dependence. By using numerical results and simulated data, we show that this approximation performs very well. We use this result to construct a binary market model driven by this process and we show that the model admits arbitrage opportunities.

Suggested Citation

  • Ciprian Tudor & Soledad Torres, 2007. "Donsker theorem for the Rosenblatt process and a binary market model," Papers math/0703085, arXiv.org.
    • Handle: RePEc:arx:papers:math/0703085
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    File URL: http://arxiv.org/pdf/math/0703085
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    Cited by:

    1. Nikolai Dokuchaev, 2013. "On strong binomial approximation for stochastic processes and applications for financial modelling," Papers 1311.0675, arXiv.org, revised Feb 2015.

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