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. 

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

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

Please log in with your WU account to use all functionalities of read!t. For off-campus access to our licensed electronic resources, remember to activate your VPN connection connection. In case you encounter any technical problems or have questions regarding read!t, please feel free to contact the library at readinglists@wu.ac.at.