2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114028This 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.53 pagesProbability60G48; 60H05; 60H07; 60H10text