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.
Content requirements
Contents
- Set systems, Caratheodory's theorem
- d-dimensional Lebesgue measure
- Measurable functions, integral with respect to a measure, convergence theorems
- L_p-spaces
- Product measures, Fubini's theorem
- transformation theorem
- weak convergence, Fourier transform
- Radon-Nikodym theorem
Contact time
Number of SWS: 2 hours (V) + 1 hour (Ü)
Language of instruction: German
Subsequent courses
Module handbook
KIS
OLAT
Content requirements
Contents
- The basic concepts of financial mathematics in discrete time are covered:
- One-period model,
- Stochastic modeling of financial markets,
- Risk-neutral valuation,
- Fundamental theorems of price theory.
Contact time
Number of SWS: 2 hours (V)
Language of instruction: German
Info: The lecture takes place in blocks in the first half of the semester .
Follow-up courses
Module handbook
KIS
OLAT
Content requirements
Contents
- The main principles of modern continuous time financial mathematics such as
- the no arbitrage principle,
- the replication principle,
- the risk-neutral valuation principle
- The continuous-time financial market model in a diffusion setting which is based on deep technical results and methods such as
- Brownian motion and martingales
- Itô integrals and Itô calculus including Itô's formula, Itô's martingale representation theorem, Girsanov' theorem and the Feynman-Kac theorem
- Stochastic differential equations
- Parabolic partial differential equations
- The martingale and the PDE approach to option pricing including the Black-Scholes formula and some practical applications
- Valueing various exotic options including some basic numerical schemes to price them
- Solving the continuous-time portfolio optimization problem by the martingale approach
Contact time
Number of SWS: 4 hrs (V) + 2 hrs (Ü)
Language of instruction: English
Follow-up courses
Module handbook
KIS
OLAT
Content requirements
Contents
- Introduction to portfolio optimization (problem definition),
- Continuous-time portfolio problem: expected utility approach,
- Martingale method in complete markets,
- Stochastic control approach (HJB equation, verification theorems),
- Portfolio optimization with restrictions (e.g. risk barriers, transaction costs),
- Comparison with mean-variance optimization (Markowitz),
- Portfolio optimization with derivatives,
- Alternative methods.
Contact time
Number of SWS: 2 hours (V)
Language of instruction: English
Module handbook
KIS
OLAT
(Project) seminars
Content requirements
Contents
Working on a project from the practice of the finance and insurance industry in a project group (2-5 participants) under the guidance of a project supervisor:
- The starting point is a real problem.
- Problem processing: selection or development of a suitable financial or actuarial model, classification in the theoretical background, formulation of solution approaches, development of theoretical solutions or selection of suitable numerical methods, implementation of the methods. In regular meetings with the supervisors, one group member presents the current status of the work and the plans for the next steps.
- Final presentation and/or final report on the project, with each member of the project group being responsible for one part.
The exact content will be presented in a preliminary meeting (date to be announced).
Contact time
Number of SWS: 2 hours Project supervision
Language of instruction: German/English (as required)
Dates
The exact dates will be announced. (no regular date)
Module handbook
KIS
Content requirements
Contents
- Modeling of discrete-time financial markets,
- Application of concepts of probability theory: conditional expected value, martingales, stopping times, change of measure,
- binomial model,
- Price theory in discrete-time financial markets,
- Valuation of European options,
- Valuation of American options,
- Basics of portfolio optimization.
Contact time
Number of SWS: 2 hours Project supervision
Language of instruction: English
Course dates
- Wed (01.04. 15:30 - 17:30) in room 48-538
- Thu (02.04. 16:45 - 18:45) in room 48-538
- Tue (07.04. 15:30 - 17:30) in room 48-538
- Wed (08.04. 15:30 - 17:30) in room 48-538
Module handbook
KIS
Content requirements
Contents
Working on an advanced topic at Master's level from the field of financial mathematics.
Contact time
Number of SWS: 2 hours Project supervision
Language of instruction: English
Registration and deadlines
Please register by e-mail to Prof. Dr. Saß by April 13. Please indicate in this e-mail which lectures in financial and actuarial mathematics you have attended.
First meeting on April 16, 11:45 a.m., room 48-606. The times for the weekly meetings will then be discussed. (no regular date)
Module handbook
KIS
Content requirements
Contents
Lectures by PhD students at RPTU/Promovierende am ITWM in the field of financial mathematics on their respective research topics.
Contact time
Number of SWS: 2 hours Project supervision
Language of instruction: German/English (as required)
Registration and dates
If you are interested, please send an e-mail to Dr. Laudage by April 13. Please indicate in this e-mail which lectures in financial and actuarial mathematics you have attended.
The meetings take place (irregularly) on Wednesdays at 12:00 noon at the ITWM. Prior registration is therefore mandatory for participation.
KIS
Reading Course(s)
Content requirements
Contents
Worst-case portfolio optimization
The exact contents will be presented in a preliminary talk at the beginning of the semester (date of a meeting to be announced).
Contact time
Number of SWS: 2 hours Project supervision
Language of instruction: German/English (as required)
Registration and dates
Please send an e-mail to Prof. Dr. Korn by April 13. Please indicate in this e-mail which lectures in financial and actuarial mathematics you have attended.
The exact dates will be announced. (no regular date)
Module handbook