2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212716These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis.Computational FinanceProbabilityFrom Black-Scholes and Dupire formulae to last passage times of local martingales. Part A : The infinite time horizontext