Time and place

Lecture: Fr, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, every other week, various dates
Sir-in Exam: Date to be announced

Teacher: Thorsten Schmidt
Language: in German

Stochastic is, to put it loosely, the “mathematics of chance”, about which---possibly contrary to first impressions---many precise and not at all random statements can be formulated and proven. The aim of the lecture is to give an introduction to stochastic modeling, to explain some basic concepts and results of Stochastic and to illustrate them with examples. It is also intended as a motivating preparation for the lecture “Probability Theory” in the summer semester, especially for students in the B.Sc. in Mathematics. Topics covered include: Discrete and continuous random variables, probability spaces and measures, combinatorics, expected value, variance, correlation, generating functions, conditional probability, independence, weak law of large numbers, central limit theorem. The lecture Elementary Probability Theory~II in the summer semester will mainly be devoted to statistical topics. If you are interested in a practical, computer-supported implementation of individual lecture contents, participation in the regularly offered practical excercise “Praktischen Übung Stochastik" is also recommended (in parallel or subsequently).

Required: Linear Algebra~I, Analysis~I and II. \ Note that Linear Algebra~I can be attended in parallel.

Elementary Probabilty Theory (2HfB21, MEH21)
Elementary Probability Theory I (BSc21, MEB21, MEdual24)

Time and place

Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Computer exercise: 2 hours, date to be determined

Teacher: Sören Bartels, Moritz Diehl, Thorsten Schmidt
Language: in English

This course provides an introduction into the basic concepts, notions, definitions and results in probability theory, numerics and optimization, accompanied with programming projects in Python. Besides deepen mathematical skills in principle, the course lays the foundation of further classes in these three areas.

None that go beyond admission to the degree programme.

Basics in Applied Mathematics (MScData24)

Time and place

Lecture: Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined

Teacher: Thorsten Schmidt
Assistant: Simone Pavarana
Language: in English

In this lecture we will study new and highly efficient tools from machine learning which are applied to stochastic problems. This includes neural SDEs as a generalisation of stochastic differential equations relying on neural networks, transformers as a versatile tool not only for languages but also for time series, transformers and GANs as generator of time series and a variety of applications in Finance and insurance such as (robust) deep hedging, signature methods and the application of reinforcement learning.

The prerequisites are stochastics, for some parts we will require a good understanding of stochastic processes. A (very) short introduction will be given in the lectures – so for fast learners it would be possible to follow the lectures even without the courses on stochastic processes.

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)

Time and place

Lecture: Mo, 10-12h, HS 00-036, Georges-Köhler-Allee 101
Tutorial: 2 hours, various dates

Teacher: Thorsten Schmidt

Time and place

Lecture: Mo, Mi, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined

Teacher: Thorsten Schmidt
Assistant: Moritz Ritter
Language: in English

This lecture marks the culmination of our series on probability theory, achieving the ultimate goal of this series: the combination of stochastic analysis and financial mathematics---a field that has yielded an amazing wealth of fascinating results since the 1990s. The core is certainly the application of semimartingale theory to financial markets culminating in the fundamental theorem of asset pricing. This results is used everywhere in financial markets for arbitrage-free pricing.

After this we look into modern forms of stochastic analysis covering neural SDEs, signature methods, uncertainty and term structure models. The lecture will conclude with an examination of the latest applications of machine learning in financial markets and the reciprocal influence of stochastic analysis on machine learning.

Required: Probability Theory II (Stochastic Processes)

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Advanced Lecture in Stochastics (MScData24)
Elective in Data (MScData24)

Time and place

Seminar: Fr, 10-12h, SR 125, Ernst-Zermelo-Str. 1
Preregistration:
Preliminary Meeting 18.10.
Preparation meetings for talks: Dates by arrangement

Teacher: Thorsten Schmidt
Assistant: Moritz Ritter
Language: Talk/participation possible in German and English

This seminar will focus on theoretical machine learning results, including modern universal approximation theorems, approximation of filtering methods through transformes, application of machine learning methods in financial markets and possibly other related topics. Moreover, we will cover topics in stochastic analysis, like fractional Ito calculus, uncertainty, filtering and optimal transport. You are also invited to suggest related topics.

Required: Basic Probability and either Machine Learning or Probability Theory II (Stochastic Processes).

Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Mathematical Seminar (MScData24)
Elective in Data (MScData24)

Time and place

Lecture: Fr, 10-12h, SR 226, Hermann-Herder-Str. 10, Do, 12-14h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Thorsten Schmidt
Assistant: Moritz Ritter

Time and place

Mi, 16-17h, HS II, Albertstr. 23b

Teacher: David Criens, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Time and place

Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b

Teacher: Thorsten Schmidt
Assistant: Moritz Ritter
general:

Compulsory Elective in Mathematics (BSc21)

Time and place

Mi, 16-17h, SR 226, Hermann-Herder-Str. 10

Teacher: David Criens, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, SR 125, Ernst-Zermelo-Str. 1

Teacher: Harald Binder, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Time and place

Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
Sit-in exam (resit) 11.10., 09:15-10:45
26.07., 09:15-10:45

Teacher: Thorsten Schmidt
Assistant: Moritz Ritter
general:

Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Applied Mathematics (MSc14)

Time and place

Lecture: Di, 10-12h, SR 226, Hermann-Herder-Str. 10

Teacher: Thorsten Schmidt
Assistant: Lars Niemann
general:

Time and place

Do, 10-12h, SR 125, Ernst-Zermelo-Str. 1

Teacher: Peter Pfaffelhuber, Thorsten Schmidt
Assistant: Ernst August von Hammerstein

Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)

Time and place

Fr, 13-14h, HS II, Albertstr. 23b

Teacher: David Criens, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, HS II, Albertstr. 23b

Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Time and place

Lecture: Fr, 10-12h, HS Weismann-Haus, Albertstr. 21a
29.07., 10:00-12:00

Teacher: Thorsten Schmidt
Assistant: Moritz Ritter
general: ,

Compulsory Elective in Mathematics (BSc21)

Time and place

Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
25.07., 12:00-14:00
Sit-in exam (resit) 13.10., 10:00-12:00

Teacher: Thorsten Schmidt
Assistant: Moritz Ritter
general:

Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Applied Mathematics (MSc14)

Time and place

Fr, 13-14h, HS II, Albertstr. 23b

Teacher: Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, HS II, Albertstr. 23b

Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Time and place

Lecture: Fr, 10-12h, HS Weismann-Haus, Albertstr. 21a
22.02., 00:00-00:00
Sit-in exam (resit) 29.07., 10:00-12:00

Teacher: Thorsten Schmidt
Assistant: Moritz Ritter
general: ,

Elementary Probability Theory I (BSc21, MEB21, MEdual24)
Elementary Probabilty Theory (2HfB21, MEH21)

Teacher: Thorsten Schmidt
Assistant: Moritz Ritter
general:

Compulsory Elective in Mathematics (BSc21)

Time and place

Di, 10-12h, SR 125, Ernst-Zermelo-Str. 1

Teacher: Thorsten Schmidt
Assistant: Lars Niemann

Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)

Time and place

Fr, 13-14h, HS II, Albertstr. 23b

Teacher: Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, HS II, Albertstr. 23b

Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Teacher: Thorsten Schmidt
Assistant: Moritz Ritter
general:

Compulsory Elective in Mathematics (BSc21)

Time and place

Mo, 12-14h, , online

Teacher: Thorsten Schmidt
Assistant: Lars Niemann

Supplementary Module in Mathematics (MEd18)
Compulsory Elective in Mathematics (BSc21)

Time and place

Fr, 13-14h, -, -

Teacher: Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, -, -

Teacher: Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Lecture: Mo, Do, 10-12h, genauere Informationen zum Ablauf durch Dozenten nach Belegung in HISinOne, -

Teacher: Thorsten Schmidt
Assistant: Lars Niemann, Moritz Ritter
general:

Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)

Time and place

Lecture: Mi, Mo, 12-14h, , online

Teacher: Thorsten Schmidt
Assistant: Moritz Ritter
general:

Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)

Time and place

Fr, 13-14h, , online

Teacher: Peter Pfaffelhuber, Philipp Harms, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, , online

Teacher: Harald Binder, Philipp Harms, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Time and place

Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
Sit-in exam (resit) 28.10., 10:00-00:00

Teacher: Thorsten Schmidt
Assistant: Marc Weber
general:

Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Applied Mathematics (MSc14)
Mathematical Concentration (MEd18, MEH21)

Time and place

Lecture: Mo, 14-16h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Thorsten Schmidt
Assistant: Lars Niemann
general:

Compulsory Elective in Mathematics (BSc21)

Time and place

Fr, 13-14h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Philipp Harms, Angelika Rohde, Thorsten Schmidt, Peter Pfaffelhuber

Time and place

Fr, 12-13h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Harald Binder, Philipp Harms, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Time and place

Lecture: Mo, Mi, 12-14h, HS Weismann-Haus, Albertstr. 21a
11.03., 10:00-12:00
Sit-in exam (resit) 08.06., 12:00-15:00

Teacher: Thorsten Schmidt
Assistant: Marc Weber, Tolulope Fadina
general:

Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Applied Mathematics (MSc14)

Time and place

Fr, 13-14h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Philipp Harms, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer, Philipp Harms

Time and place

Lecture: Mo, 14-16h, HS Rundbau, Albertstr. 21
09.09., 12:00-15:00
Sit-in exam (resit) 14.10., 10:00-13:00

Teacher: Thorsten Schmidt
Assistant: Marc Weber
general: , ,

Elementary Probabilty Theory (2HfB21, MEH21)

Teacher: Philipp Harms, Angelika Rohde, Thorsten Schmidt

Compulsory Elective in Mathematics (BSc21)

Time and place

Mi, 14-16h, SR 125, Ernst-Zermelo-Str. 1

Teacher: Thorsten Schmidt
Assistant: Marc Weber

Compulsory Elective in Mathematics (BSc21)

Time and place

Fr, 13-14h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Angelika Rohde, Thorsten Schmidt

Time and place

Lecture: Mo, 14-16h, HS Weismann-Haus, Albertstr. 21a

Teacher: Thorsten Schmidt
Assistant: Wahid Khosrawi
general: , ,

Elementary Probabilty Theory (2HfB21, MEH21)

Time and place

Fr, 13-14h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Philipp Harms, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt