Modeling financial assets without semimartingales
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 selffinancing, previous prices are forced to be finite quadratic variation processes. The nonarbitrage 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606642
 Bibcode:
 2006math......6642C
 Keywords:

 Mathematics  Probability;
 60G48;
 60H05;
 60H07;
 60H10
 EPrint:
 53 pages