This talk does not suppose a priori that the evolution of a financial asset price is a semimartingale. The stochastic integral intervening in the definition of self-financing property is forward integral. If one requires that a certain minimal class of investor strategies are self-financing, previous prices are forced to be finite quadratic variation processes. The non-arbitrage property is not excluded if the class of admissible strategies is restricted. The classical notion of martingale is replaced with the notion of -martingale. Two instruments are developed: a calculus related to -martingales and infinite dimensional integration via regularization, with some examples. Some applications to no-arbitrage, viability, hedging and the maximization of the utility of an insider are expanded. The talk is essentially based on a joint work with Rosanna Coviello. Francesco RUSSO. Université Paris 13. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182789707066 (pdf) Bande son disponible au format mp3 Durée : 55 mn