This course provides a rigorous introduction to the It么 Stochastic Calculus, with applications to Mathematical Finance. Topics include: measure-theoretic probability, discrete and continuous-time martingales and stopping times, Doob's Optional Sampling Theorem and Maximal Inequalities, martingale convergence theorems, Brownian motion, predictable processes, the It么 stochastic integral, local martingales and semimartingales, the quadratic variation process of a local martingale, the It么 formula, applications to mathematical finance (the Black-Scholes equation for option pricing, the Greeks).
This course provides a rigorous introduction to the It么 Stochastic Calculus, with applications to Mathematical Finance. Topics include: measure-theoretic probability, discrete and continuous-time martingales and stopping times, Doob's Optional Sampling Theorem and Maximal Inequalities, martingale convergence theorems, Brownian motion, predictable processes, the It么 stochastic integral, local martingales and semimartingales, the quadratic variation process of a local martingale, the It么 formula, applications to mathematical finance (the Black-Scholes equation for option pricing, the Greeks).
