On stochastic calculus related to financial assets without semimartingales
july, 2011
Publication type:
Paper in peer-reviewed journals
Journal:
Bulletin Sciences Mathématiques, vol. 135, pp. 733774
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Keywords :
$A$-martingale; weak $k$-order Brownian motion;
no-semimartingale; utility maximization; insider; no-arbitrage;
viability; hedging
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 $A$ of admissible strategies
is restricted. The classical notion of martingale is replaced with the notion
of $A$-martingale. A calculus related to $\sha$-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.
BibTeX:
@article{Cov-DiG-Rus-2011, author={Rosanna Coviello and Cristina Di Girolami and Francesco Russo }, title={On stochastic calculus related to financial assets without semimartingales }, doi={10.1016/j.bulsci.2011.06.008 }, journal={Bulletin Sciences Mathématiques }, year={2011 }, month={7}, volume={135 }, pages={733774}, }