Algebra (LA Gym) (Gerkmann)

Analysis mehrerer Variablen (LA Gym) (Gerkmann)

Complex Geometry (Stelzig, Gritschacher)

Computational Finance and its Object-Oriented Implementation (with Application to Interest-Rates and Hybrid Models)

Oberseminar: Topics in Algebra and Algebraic Geometry (Rosenschon, Weinzierl)

Oberseminar: Arithmetische und Algebraische Geometrie (Rosenschon, Weinzierl)

Algebraische Geometrie I (Rosenschon, Weinzierl)

In diesem Modul wird in die Algebraische Geometrie, insbesondere in die Theorie der algebraischen Varietäten und/oder Schemata und ihrer Morphismen eingeführt. Es werden affine und projektive Varietäten bzw. Schemata studiert und grundlegende Eigenschaften untersucht, insbesondere Dimension, Morphismen und birationale Abbildungen.

Seminar: Morse theory (Bauer, Vogel)

Topology 1 (Vogel, Boeke)

Beginning with a very limited dicussion of point set topology I plan to discuss the fundamental group and covering spaces. After that, we move to singular homology and its applications. The lecture topolgy 2 in the summer term will continue with holomgy and cohomology. 

Differentiable manifolds (Differential geometry I) (Leeb, Zoller)

Finanzmathematik in diskreter Zeit (Gonon/Walter)

Stochastic Processes (Caicedo, Heydenreich)

Finanzmathematik II / Stochastic Calculus and Arbitrage Theory in Continuous Time

The lecture provides an introduction to stochastic calculus with an emphasis on the mathematical concepts that are later used in the mathematical modeling of financial markets.

In the first part of the lecture course the theory of stochastic integration with respect to Brownian motion and Ito processes is developed. Important results such as Girsanov's theorem and the martingale representation theorem are also covered. The first part concludes with a chapter on the existence and uniqueness of strong and weak solutions of stochastic differential equations.

The second part of the lecture course gives an introduction to the arbitrage theory of financial markets in continuous time driven by Brownian motion. Key concepts are the absence of arbitrage, market completeness, and the risk neutral pricing and hedging of contingent claims. Particular attention will be given to the the Black-Scholes model and the famous Black-Scholes formula for pricing call and put options.

If you wish to participate in the course, please sign up as soon as possible by sending an e-mail from your LMU e-mail address to Annika Steibel (steibel@math.lmu.de).


Computergestützte Mathematik (Reisser)

Optimierung (Perkkiö, Reisser)

Lineare Algebra I (Panagiotou)