Introduction to mathematical theories, which are applied in financial and actuarial mathematics. Each chapter will be motivated and recent results will be presented.

Theorie of polish spaces, notions of convergence in pronbability theory, martingales in discrete and continuous time, Gaussian processes, Brownian motion, stochastic integration with respect to continuous semimartingales, Ito's formula, Girsanov's theorem, stochastic differential equations, Introduction to Malliavin Calculus, Clarc-Ocone Formula, Hoermander's theorem, Poisson process, general theory of stochastic processes, Levy-processes

oral exam

Oksendal: Stochastic Differential Equations: An Introduction with Applications More literature will be told in the lecture.

probability theory, measure theory, analysis, linear algebra, functional analysis