Modeling financial assets without semimartingale

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 $\cal{A}$ of admissible strategies is restricted. The classical notion of martingale is replaced with the notion of $\cal{A}$-martingale. A calculus related to $\cal{A}$ -martingales with some examples is developed. Some applications to the maximization of the utility of an insider are expanded.
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Submitted on : Monday, June 26, 2006 - 8:20:34 PM
Last modification on : Wednesday, February 6, 2019 - 1:23:55 AM
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Rosanna Coviello, Francesco Russo. Modeling financial assets without semimartingale. 2006. ⟨hal-00082050⟩

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