The present research proposal deals with applications of the theory of stochastic processes to foundational issues in mathematical finance. We plan to investigate non-classical no-arbitrage-type conditions, which in particular allow to go beyond the usual risk-neutral paradigm of quantitative finance, by relaxing the classical No Free Lunch with Vanishing Risk (NFLVR) condition. To this effect, we shall make use of deep results from the general theory of stochastic processes. By relying on the theory of the enlargement of filtrations, we shall also study the behavior of weak no-arbitrage-type conditions with respect to changes of the information available to market participants, thus allowing the study of insider trading and limited information phenomena in relation with non-classical no-arbitrage-type conditions. We shall apply these results to the specific context of credit risk modelling. This analysis will provide guidance towards the development of a new generation of financial models which can overcome some of the limitations of the existing ones. The research activity will be carried out at the Department of Mathematics of the University of Evry (France, Paris area), within the research group coordinated by Prof. Monique Jeanblanc. By its own nature, the present research project has a strong inter-disciplinary character, being at the intersection between stochastic analysis, finance and economic theory.