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...Stochastic calculus and applications to finance scaf pierre etore master msiam track data science year contents processes brownian motion general denitions properties markov continuous time martingales rst afundamental process the of nite variation quadratic functions integration it o formula l evy girsanov theorems exponential martingale theorem dierential equations link with partial dif ferential introduction motivations one dimensional black scholes model adigression on sde self nancing portfolio risk neutral probability measure construction replicating pricing hedging formulae pde appendix bibliography...