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.

2020S, VO, 2.0h, 4.0EC

Properties

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

Learning outcomes

After successful completion of the course, students are able to...

reflect and explain the theory as well as to apply the learned skills in practice (this is a standard text, which will be updated during September 2019).

Subject of course

Chain rule and convergence theorems for stochastic integrals (with respect to continuous semimartingales), integration by parts, multi-dimensional Ito formula with applications, Tanaka's formula, local Ito formula and Ito formula for holomorphic functions, complex exponential local martingales, Lévy's characterization of standard Brownian motion, Girsanov's theorem, stochastic exponential of continuous local martingales, removal of drift using Girsanov's theorem, Doob's upcrossing inequality, Doob's convergence theorems for submartingales, representation of Brownian local martingales, Kazamaki's and Novikov's criterion, Novikov's local criterion

Teaching methods

The basic contents and concepts are presented by the head of the LVA and illustrated and discussed with the help of examples.

Mode of examination

Oral

Lecturers

Institute

Course dates

DayTimeDateLocationDescription
Thu09:00 - 11:0005.03.2020 - 25.06.2020Sem.R. DA grün 06A .
Thu11:00 - 12:0005.03.2020 - 23.04.2020Sem.R. DA grün 06A .
Stochastic analysis in financial and actuarial mathematics 2 - Single appointments
DayDateTimeLocationDescription
Thu05.03.202009:00 - 11:00Sem.R. DA grün 06A .
Thu05.03.202011:00 - 12:00Sem.R. DA grün 06A .
Thu12.03.202009:00 - 11:00Sem.R. DA grün 06A .
Thu12.03.202011:00 - 12:00Sem.R. DA grün 06A .
Thu19.03.202009:00 - 11:00Sem.R. DA grün 06A .
Thu19.03.202011:00 - 12:00Sem.R. DA grün 06A .
Thu26.03.202009:00 - 11:00Sem.R. DA grün 06A .
Thu26.03.202011:00 - 12:00Sem.R. DA grün 06A .
Thu02.04.202009:00 - 11:00Sem.R. DA grün 06A .
Thu02.04.202011:00 - 12:00Sem.R. DA grün 06A .
Thu23.04.202009:00 - 11:00Sem.R. DA grün 06A .
Thu23.04.202011:00 - 12:00Sem.R. DA grün 06A .
Thu30.04.202009:00 - 11:00Sem.R. DA grün 06A .
Thu07.05.202009:00 - 11:00Sem.R. DA grün 06A .
Thu14.05.202009:00 - 11:00Sem.R. DA grün 06A .
Thu28.05.202009:00 - 11:00Sem.R. DA grün 06A .
Thu04.06.202009:00 - 11:00Sem.R. DA grün 06A .
Thu18.06.202009:00 - 11:00Sem.R. DA grün 06A .
Thu25.06.202009:00 - 11:00Sem.R. DA grün 06A .

Examination modalities

The performance is assessed by an oral examination at the end of the semester.

Course registration

Not necessary

Curricula

Literature

Registered students (to part 1 of the course) have access to an English script in electronic format with numerous references. The script will be updated on a continuing basis.

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

Foundations:
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

Continuative courses

Language

if required in English