Introduction to stochastic analysis as needed for continuous-time financial and actuarial mathematics.
Review of basic definitions from probability theory, continuity theorem of Levy, definition and basic properties of the multi-dimensional normal distribution, Brownian motion/Wiener process, Gaussian processes, existence proof of Brownian motion, definition of the Itô integral, Itô isometry, martingales and martingale inequalities, basic properties of the Itô integral, one- and multi-dimensional Itô formula, martingale representation
Oral exam