6047 Convex Analysis
Univ.Prof. Dipl.Wirtsch.-Math.Dr. Birgit Rudloff
Contact details
Weekly hours
Language of instruction
02/20/23 to 03/03/23
Registration via LPIS
Notes to the course
Day Date Time Room
Wednesday 03/08/23 03:30 PM - 06:00 PM D4.0.047
Tuesday 03/14/23 09:00 AM - 11:00 AM D4.0.047
Tuesday 03/21/23 09:00 AM - 11:30 AM D4.0.047
Tuesday 03/28/23 09:00 AM - 11:30 AM D4.0.047
Tuesday 04/11/23 09:00 AM - 11:30 AM D4.0.047
Tuesday 04/18/23 09:00 AM - 11:30 AM D4.0.047
Tuesday 04/25/23 09:00 AM - 11:30 AM D4.0.047
Tuesday 05/02/23 09:00 AM - 11:30 AM D4.0.047
Tuesday 05/09/23 09:00 AM - 11:30 AM D4.0.047

Tools from Convex Analysis, in particular duality methods, arise frequently in Mathematical Finance and Economics. In this course, we will review and motivate some basic concepts in Convex Analysis (Hahn-Banach theorem, biconjugation theorem, subdifferentials, Fenchel-Rockafellar duality theorem) on infinite dimensional spaces.

These tools are going to be applied to a special type of functions which frequently appears in Finance and Economics, in particular when it comes to pricing, risk evaluation or utility measurement. Examples are coherent and convex risk measures, no arbitrage price bounds, good deal bounds and optimized certainty equivalents, among many others. Duality concepts will be discussed and examples including risk measures, portfolio optimization, the Fundamental Theorem of Asset Pricing, hedging and capital/risk allocation problems will be studied. 

Learning outcomes
The students should become familiar with basic tools from infinite dimensional Convex Analysis and be able to apply them, in particular to problems in Economics and Financial Mathematics.
Attendance requirements

Full attendance is compulsory. This means that students should attend at least 80% of all lectures, at most one lecture can be missed.

Teaching/learning method(s)
There will be classroom lectures and assignments for the participants. Lecture notes will be posted online.

There will be homework assignments (each 15%) and a final (55%).


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Additional material on learn@WU
Lecture notes will be distributed during the course.
Last edited: 2023-03-14