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On stochastic calculus related to financial assets without semimartingales

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  • Rosanna Coviello

    (LAGA)

  • Cristina Di Girolami

    (ENSTA ParisTech, Luiss Guido Carli)

  • Francesco Russo

    (ENSTA ParisTech, INRIA Rocquencourt)

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    Abstract

    This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes. The non-arbitrage property is not excluded if the class $\mathcal{A}$ of admissible strategies is restricted. The classical notion of martingale is replaced with the notion of $\mathcal{A}$-martingale. A calculus related to $\mathcal{A}$-martingales with some examples is developed. Some applications to no-arbitrage, viability, hedging and the maximization of the utility of an insider are expanded. We finally revisit some no arbitrage conditions of Bender-Sottinen-Valkeila type.

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    File URL: http://arxiv.org/pdf/1102.2050
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1102.2050.

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    Date of creation: Feb 2011
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    Publication status: Published in Bulletin des Sciences Math\'ematiques 135 (2011) 733-774
    Handle: RePEc:arx:papers:1102.2050

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    1. Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October.
    2. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
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    Cited by:
    1. Cristina Girolami & Giorgio Fabbri & Francesco Russo, 2014. "The covariation for Banach space valued processes and applications," Metrika, Springer, vol. 77(1), pages 51-104, January.

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