105.091 Stochastic analysis in financial and actuarial mathematics 2
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2015S, VO, 2.0h, 4.0EC


  • Semester hours: 2.0
  • Credits: 4.0
  • Type: VO Lecture

Aim of course

Stochastic analysis as needed for continuous-time financial and actuarial mathematics.

Subject of course

Martingale representation, Gronwall's inequality, examples and solution methods for stochastic differential equations, existence and uniqueness theorem, Yamada-Watanabe condition, weak and strong solutions, Bayes' formula, Lévy's characterization of Brownian motion, several versions of Girsanov's theorem, exponential martingales, Kazamaki's criterion, Novikov's condition, Doob-Meyer decomposition, Itô diffusions, Markov property, strong Markov property, generator of an Itô diffusion, Dynkin's formula, applications



Course dates

Thu09:00 - 11:1505.03.2015 - 25.06.2015Sem.R. DA grün 06A .
Stochastic analysis in financial and actuarial mathematics 2 - Single appointments
Thu05.03.201509:00 - 11:15Sem.R. DA grün 06A .
Thu12.03.201509:00 - 11:15Sem.R. DA grün 06A .
Thu19.03.201509:00 - 11:15Sem.R. DA grün 06A .
Thu26.03.201509:00 - 11:15Sem.R. DA grün 06A .
Thu16.04.201509:00 - 11:15Sem.R. DA grün 06A .
Thu23.04.201509:00 - 11:15Sem.R. DA grün 06A .
Thu30.04.201509:00 - 11:15Sem.R. DA grün 06A .
Thu07.05.201509:00 - 11:15Sem.R. DA grün 06A .
Thu11.06.201509:00 - 11:15Sem.R. DA grün 06A .
Thu25.06.201509:00 - 11:15Sem.R. DA grün 06A .

Examination modalities

oral exam

Course registration

Not necessary



Bernt Øksendal: Stochastic Differential Equations: An Introduction with Applications. 6. Edition, Springer-Verlag, 2007, ISBN 978-3-54004-758-2.

Additional literature:
Olav Kallenberg: Foundations of Modern Probability. 2. Edition, Springer-Verlag, 2002, ISBN 0-387-953113-2.
Daniel Revuz and Marc Yor: Continuous Martingales and Brownian Motion, 3. Edition, Springer-Verlag, 1999, ISBN 3-540-64325-7.
Ioannis Karatzas und Steven E. Shreve: Brownian Motion and Stochastic Calculus. 2. Edition, Springer-Verlag, ISBN 0-38797-655-8.

David Williams: Probability with Martingales. Cambridge University Press, 1991, ISBN 0-521-40605-6.
Heinz Bauer: Maß- und Integrationstheorie. 2. Edition, De Gruyter, 1992, ISBN 3-11013-626-0.
Heinz Bauer: Wahrscheinlichkeitstheorie. 5. Edition, De Gruyter, 2002, ISBN 3-11017-236-4.

Preceding courses

Accompanying courses