2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164296These notes are the second half of the contents of the course given by the second author at the Bachelier Seminar (8-15-22 February 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis.ProbabilityFrom Black-Scholes and Dupire formulae to last passage times of local martingales. Part B : The finite time horizontext