General information
Below you find a list of the lectures that our group offers in the winter term 2021/2022.
If you would like to participate in a seminar, project seminar (see registration form) or reading course during the winter term, please inform the respective person in charge by e-mail. Dates will be agreed upon together with the participants.
If you are interested in writing a thesis in our group, just get in touch with your favored supervisor.
Probability Concepts for Financial Markets
Contents
- Modeling of discrete-time financial markets
- Review and extensions of concepts from probability: Conditional expectation, martingales, stopping times, change of measure
- Binomial model
- Pricing of financial products in discrete-time financial markets
- European options
- American options
- Basics of portfolio optimization
Frequency of occurrence
The intensive course takes place every semester in the last week before the lecture period starts.
Here you find the KIS entry: Probability Concepts for Financial Markets (compact course)
Here you find the OLAT course: TUK Probability Concepts for Financial Markets WS 21/22
Non-Life Insurance Mathematics
Contents
- Convolution and transforms
- Claim size distributions
- Individual risk model
- Collective risk models:
- Claim number process
- Poisson process
- Renewal processes
- Total claim size distribution
- Risk Process
- Ruin theory and ruin probabilities
- Premium calculation
- Experience rating:
- Bayes estimation
- Linear Bayes estimation (Bühlmann and Bühlmann-Straub model)
- Reserves
- Reinsurance and risk sharing
Frequency of occurrence
The lecture is offered every year in the winter term.
Here you find the KIS entry: Non-Life Insurance Mathematics (lecture)Non-Life Insurance Mathematics (tutorial)
Here you find the OLAT course: TUK Non-Life Insurance Mathematics WS 21/22
Interest Rate Theory
Contents
- Basics of interest modelling (Bonds and linear products, swaps, caps and floors, bond options, rate of interest options, interest rate term structure curve, interest rates (short rates and forward rates))
- Heath-Jarrow-Morton framework (simple example: Ho-Lee model, general HJM drift condition, one- and multidimensional modelling)
- Short rate models (general one factor-modelling, term structure equation, affine modelling of interest rate structure, Vasicek-, Cox-Ingersoll-Ross- and further models, option pricing model, model calibration )
- Defaultable bonds (Merton model)
Frequency of occurrence
The lecture is offered every year in the winter term.
Here you find the KIS entry: Interest Rate Theory (lecture)
Here you find the OLAT course: TUK Interest Rate Theory WS 21/22
Continuous-Time Portfolio Optimization
Contents
- Introduction to portfolio optimization (problem statement)
- Continuous-time portfolio problem: expected benefit approach
- Martingale method for complete markets
- Stochastic control approach (HJB equation, verification theorems)
- Portfolio optimization with restrictions (e.g. risk boundaries, transaction costs)
- Alternative methods
Frequency of occurrence
The lecture is offered irregularly in the winter term.
Here you find the KIS entry: Continuous-Time Portfolio Optimization (lecture)
Here you find the OLAT course: TUK Continuous-Time Portfolio Optimization WS 21/22
Seminars and Reading Course
Our group offers the following additional courses in the winter term 2021/22:
Seminar: Actuarial and Financial Mathematics
Dates
Please contact Prof. Dr. Jörn Sass by e-mail. Dates will then be agreed upon together with the participants.
Here you find the OLAT course: TUK Seminar Actuarial and Financial Mathematics WS 21/22
Reading Course: Advanced Topics in Actuarial and Financial Mathematics
Dates
Please contact Prof. Dr. Ralf Korn by e-mail. Dates will then be agreed upon together with the participants.
Here you find the OLAT course: TUK Advanced Topics in Actuarial and Financial Mathematics WS 21/22