General information
Below is a list of the lectures and supplementary courses offered by our working group in the current semester.
If you would like to participate in a project seminar (see registration form) or reading course, please contact the respective supervisor by e-mail. Dates will be set in consultation with the participants.
If you would like to write a thesis in our working group, simply contact the desired supervisor directly.
Prerequisites
Course Content
- Fundamentals of Interest Rate Modeling (bonds and linear products, swaps, caps and floors, bond options, interest rate options, yield curve, interest rates (spot and forward rates)),
- Heath-Jarrow-Morton (HJM) framework (simple example: Ho-Lee model, general HJM drift condition, one- and multidimensional modeling),
- Spot Rate Models (general single-factor modeling, general valuation equation, affine yield curve modeling, Vasicek, Cox-Ingersoll-Ross, and other models, option pricing formulas, model calibration),
- Bonds Subject to Default Risk (Merton Model).
Class Time
Number of contact hours: 2 hours (V)
Language of instruction: English
Module Handbook
KIS
OLAT
Prerequisites
Topics
- Convolution and Transforms,
- Loss Distribution,
- Individual Risk Model,
- Collective Risk Models:
- Models for the number-of-claims process,
- Poisson processes,
- Renewal processes,
- Total loss distribution,
- Risk process,
- ruin theory and ruin probabilities,
- Premium calculation,
- Experience-based rating:
- Bayesian estimation,
- Linear Bayesian estimation (Bühlmann and Bühlmann-Straub models),
- Claims reserves,
- Reinsurance and risk sharing.
Class Time
Number of course hours: 4 hours (lecture) + 2 hours (exercise)
Language of instruction: English
Module Handbook
KIS
OLAT
Prerequisites
Content
- Preferences and Expected Utility,
- Axiomatic Introduction to Risk Measures,
- Robust representation of convex and coherent risk measures,
- Examples: Value at Risk, Average Value at Risk, Shortfall, Worst Case,
- Extensions: Semidynamic, dynamic, and distribution-independent risk measures,
- Estimation of risk measures,
- Rating systems:
- Score-based ratings,
- Benefit-based ratings for financial products,
- Opportunity-risk classes for insurance products,
- Credit default risks: Structural models and reduction models,
- Applications:
- Risk-based insurance premiums,
- Portfolio optimization subject to risk constraints,
- Credit derivatives.
Class Time
Number of contact hours: 2 hours (V)
Language of instruction: English
Module Handbook
KIS
OLAT
RPTU Risk Measures with Applications to Finance and Insurance Winter Semester 26/27
Prerequisites
Topics
- Asymptotic properties of M-estimators, in particular maximum-likelihood estimators,
- Bayesian and minimax estimators,
- Likelihood ratio tests: asymptotic behavior and examples (t-test, chi-squared goodness-of-fit test),
- Glivenko–Cantelli Theorem, Kolmogorov–Smirnov test,
- Differentiable statistical functionals and exemplary applications (derivation of asymptotic results, robustness),
- resampling methods using the bootstrap as an example.
Class Time
Number of SWS: 4 hours (lecture) + 2 hours (exercise)
Language of instruction: English
Module Handbook
KIS
OLAT
(Project) seminars
Prerequisites
Course Content
- Modeling time-discrete financial markets,
- Application of concepts from probability theory: conditional expected value, martingales, stopping times, change of measure,
- binomial model,
- Pricing theory in discrete-time financial markets,
- Valuation of European options,
- Valuation of American options,
- Fundamentals of portfolio optimization.
Class time
Number of SWS: 2 hours of project supervision
Language of instruction: English
Dates
- Mon (Oct. 12, 10:15 a.m. – 3:30 p.m.) in Room 48-538
- Tue (Oct. 13, 10:15 a.m. – 3:30 p.m.) in Room 48-538
- Wed (Oct. 14, 10:15 a.m. – 3:30 p.m.) in Room 48-538
- Thu (Oct. 15, 10:15 a.m. – 3:30 p.m.) in Room 48-538
- Fri (Oct. 16, 10:15 a.m. – 3:30 p.m.) in Room 48-538
Module Handbook
KIS
Prerequisites
Course Content
Study of an advanced topic at the master’s level in the field of financial mathematics.
Class Time
Number of SWS: 2 hours of project supervision
Language of instruction: English
Registration and Dates
Please register by October 17 by emailing Prof. Dr. Sass. Please indicate in this email which courses in financial and actuarial mathematics you have taken.
First meeting on October 28 at 12:00 p.m. in Room 48-606. The times for the weekly meetings will be discussed then. (No regular schedule)
Module Handbook
KIS
Prerequisites
Course Content
Working on a real-world project from the finance and insurance industry in a project group (2–5 participants) under the guidance of a project advisor:
- The starting point is a real-world problem.
- Problem-solving: Selection or development of a suitable financial or actuarial model, contextualization within the theoretical framework, formulation of solution approaches, development of theoretical solutions or selection of appropriate numerical methods, and implementation of the methods. In regular meetings with the advisors, one group member presents the current status of the work and the plan for further steps.
- Final presentation and/or final report on the project, with each member of the project group responsible for a specific section.
Core Topic: Systemic Risk
Contact Hours
Number of SWS: 2 hours of project supervision
Language of instruction: German/English (as needed)
Registration and Dates
Please register by October 17 via email with Prof. Dr. Sass. In your email, please indicate which courses in finance and actuarial science you have taken.
First meeting on October 22, 1:45–2:00 p.m., Room 48-606. The times for the weekly meetings will be discussed then. (No regular schedule)
Module Handbook
KIS
Reading Course(s)
Prerequisites
Course Content
Markov Decision Processes with Applications to Finance
The exact course content will be presented during a preliminary meeting at the beginning of the semester (the date of the meeting will be announced later).
Class Time
Number of SWS: 2 hours of project supervision
Language of instruction: German/English (as needed)
Registration and Dates
Please register by October 17 via email with Prof. Dr. Sass. In your email, please indicate which courses in finance and actuarial mathematics you have taken.
The exact dates will be announced at a later time. (No regular meeting)
Module Handbook