Advanced subjects of stochastic analysis as needed for continuous-time financial and actuarial mathematics.

Definition and examples of stochastic differential equations, strong and weak solutions, Grönwall's inequality, existence and uniqueness under Lipschitz conditions, Yamada-Watanabe condition for pathwise uniqueness, Bihari-LaSalle inequality, conditional independence, Markov property and Markov processes, independent increments and space-homogeneity, strong Markov property

oral Exam

• Bernt Øksendal: Stochastic Differential Equations: An Introduction with Applications. 6. Edition, Springer-Verlag, 2007, ISBN 978-3-54004-758-2.
• Daniel Revuz and Marc Yor: Continuous Martingales and Brownian Motion, 3. Edition, Springer-Verlag, 1999, ISBN 3-540-64325-7.
• Olav Kallenberg: Foundations of Modern Probability. 2. Edition, Springer-Verlag, 2002, ISBN 0-387-953113-2.