From Black-Scholes and Dupire formulae to last passage times of local   martingales. Part A : The infinite time horizon
  These 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. 
Amel Bentata (PMA), Marc Yor (PMA, Iuf)