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105.090
Stochastic analysis in financial and actuarial mathematics 1
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.
2011W
2010W
2009W
2008W
2007W
2006W
2009W, VO, 2.0h, 3.0EC
Properties
Semester hours: 2.0
Credits: 3.0
Type: VO Lecture
Aim of course
Introduction to stochastic analysis as needed for continuous-time financial and actuarial mathematics.
Subject of course
Review of basic definitions from probability theory, Kolmogorov's extension theorem, definition and basic properties of the multi-dimensional normal distribution, Brownian motion/Wiener process, Gaussian processes, Kolmogorov-Chentsov criterion for continuous sample paths, existence proof of Brownian motion, definition of the Itô integral, Itô isometry, martingales and martingale inequalities, basic properties of the Itô integral, existence of continuous versions, one- and multi-dimensional Itô formula, applications, martingale representation
Lecturers
Schmock, Uwe
Institute
E105 Institute of Statistics and Mathematical Methods in Economics
Course dates
Day
Time
Date
Location
Description
Mon
14:00 - 15:30
12.10.2009 - 25.01.2010
Sem.R. DA grün 03 A
SCHMOCK
Show single appointments
Stochastic analysis in financial and actuarial mathematics 1 - Single appointments
F
P
1
N
E
Day
Date
Time
Location
Description
Mon
12.10.2009
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
19.10.2009
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
26.10.2009
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
02.11.2009
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
09.11.2009
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
16.11.2009
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
23.11.2009
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
30.11.2009
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
07.12.2009
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
14.12.2009
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
21.12.2009
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
28.12.2009
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
04.01.2010
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
11.01.2010
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
18.01.2010
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
Mon
25.01.2010
14:00 - 15:30
Sem.R. DA grün 03 A
SCHMOCK
F
P
1
N
E
Examination modalities
oral exam
Course registration
Not necessary
Curricula
Study Code
Obligation
Semester
Precon.
Info
066 400 Mathematics
Mandatory elective
066 401 Statistics
Mandatory elective
066 402 Mathematics in Science and Technology
Mandatory elective
066 403 Mathematics in Economics
Mandatory elective
066 404 Mathematics in Computer Science
Mandatory elective
066 405 Financial and Actuarial Mathematics
Mandatory
1. Semester
066 405 Financial and Actuarial Mathematics
Mandatory
1. Semester
066 415 Actuarial Mathematics
Not specified
860 Technical Mathematics
Mandatory elective
864 Mathematics for Natural Sciences
Mandatory elective
866 Economic Mathematics
Mandatory elective
867 Statistics
Mandatory elective
869 Mathematics in Computer Science
Mandatory elective
873 Finance and Actuarial Mathematics
Mandatory elective
Literature
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. 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.
Accompanying courses
105.089 UE Stochastic analysis in financial and actuarial mathematics 1
Continuative courses
105.091 VO Stochastic analysis in financial and actuarial mathematics 2
105.092 UE Stochastic analysis in financial and actuarial mathematics 2
105.057 VO Mathematical Finance 2: Continuous-Time Models
105.131 UE Mathematical Finance 2: Continuous-Time Models
Language
German