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    Mean-reverting discrete time market models: Speculative opportunities and absence of arbitrage

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    Authors
    Dokuchaev, Nikolai
    Date
    2012
    Type
    Journal Article
    
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    Citation
    Dokuchaev, Nikolai. 2012. Mean-reverting discrete time market models: Speculative opportunities and absence of arbitrage. IMA Journal of Management Mathematics. 23 (1): pp. 17-27.
    Source Title
    IMA Journal of Management Mathematics
    DOI
    10.1093/imaman/dpq015
    ISSN
    1471-678X
    URI
    http://hdl.handle.net/20.500.11937/33486
    Collection
    • Curtin Research Publications
    Abstract

    In this article we study discrete time mean-reverting market models. We show that certain choices of initial conditions ensure existence of an equivalent martingale measure and absence of arbitrage for any finite time horizon. Further, it is shown that this model still allows some speculative opportunities. These opportunities cannot be expressed in the terms of arbitrage or asymptotic arbitrage. In particular, a gain can be achieved for a wide enough set of expected utilities for a strategy that does not require any hypothesis on market parameters and does not use estimation of these parameters.

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