Stochastic analysis in financial and actuarial mathematics
Additional Info
- ECTS credits: 7
- University: Vienna University of Technology
- Semester: 3
- Lecturer 1: Schmock
-
Objectives:
Introduction to stochastic analysis as needed for continuous-time financial and actuarial mathematics.
-
Topics:
Definition and properties of multi-dimensional normal distribution, definition and elementary properties of Brownian motion, existence and Hölder continuity of Brownian motion using the Kolmogorov-Chentsov continuity criterion, filtrations, stopping times, progressive measurability, path properties, martingales, uniform integrability, Vitali's convergence theorem, sub- and supermartingales, maximum inequality, Doob's inequality for p-integrable submartingales, Doob's optional sampling theorem with applications, local martingales and examples, integration of predictable step processes, p-variation of functions, quadratic variation and covariation process of continuous local martingales, Kunita-Watanabe inequality, stochastic integration for continuous local martingales and generalization for continuous semimartingales.
