On stochastic calculus related to financial assets without semimartingales

Rosanna Coviello, Cristina Di Girolami and Francesco Russo
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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.

Date: 2011-02
New Economics Papers: this item is included in nep-cis
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Citations: View citations in EconPapers (7)

Published in Bulletin des Sciences Math\'ematiques 135 (2011) 733-774

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1102.2050

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