Financial Mathematics Group

The picture shows a man in front of a blackboard with formulas.

General information

Below you find a list of the lectures that our group offers in the winter term 2022/23.

If you would like to participate in a 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.

Important links

  • KIS: dates of lectures and tutorials
  • URM: registration for tutorials
  • OpenOLAT: course materials and further information (access codes are sent by e-mail)

Lectures in the winter term

Our group offers the following lectures in the winter term 2022/23:

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

Contact time

2 SWS

Intensive course from October 17 until October 21 with integrated tutorials / seminar

Prerequisites with regard to contents

Module "Probability Theory" from the Bachelor's degree programme.

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 22/23

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

Contact time

4 SWS lecture
2 SWS tutorials

Prerequisites with regard to contents

Module "Probability Theory" from the Bachelor's degree programme.

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 22/23

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)

Contact time

2 SWS lecture

Prerequisites with regard to contents

Module "Financial Mathematics".

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 22/23

Risk Measures with Applications to Finance and Insurance

Contents

  • Preferences and expected utility
  • Axiomatic introduction of risk measures
  • Robust representation of convex and coherent risk measures
  • Examples: Value at Risk, Average Value at Risk, Short case, worst case
  • Extensions: Semi Dynamic, dynamic, distribution-free risk measures
  • Estimation of risk measures
  • Rating systems:
    • Score-based ratings
    • Utility based ratings of financial products
    • Risk-classes for insurance products
  • Credit risk: Structural models and reduced form models
  • Applications:
    • Risk-based insurance premiums
    • Portfolio optimization under risk constraints
    • Credit derivatives

Contact time

2 SWS lecture

The lecture takes place during the second half of the semester.

Prerequisites with regard to contents

Module "Financial Mathematics".

Frequency of occurrence

The lecture takes place irregularly.

Here you find the KIS entry: Risk Measures with Applications to Finance and Insurance (lecture)

Here you find the OLAT course: TUK Risk Measures with Applications to Finance and Insurance WS 22/23

Seminars and Reading Course

Our group offers the following additional courses in the winter term 2022/23:

Project Seminar: Advanced Modelling in Actuarial and Financial Mathematics

Contents

Aspects of Continuous-Time Portfolio Optimization

Contact time

2 SWS project seminar

Dates

Please contact Prof. Dr. Ralf Korn by e-mail. Dates will then be agreed upon together with the participants.

Reading Course: Advanced Topics in Actuarial and Financial Mathematics

Contents

Aspects of Continuous-Time Portfolio Optimization

Dates

Please contact Prof. Dr. Ralf Korn by e-mail. Dates will then be agreed upon together with the participants.

Here you find the KIS entry: Reading Course "Advanced Topics in Actuarial and Financial Mathematics"

Here you find the OLAT course: TUK Reading Course „Advanced Modelling in Financial and Actuarial Mathematics“ WS 22/23

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