Combinatorial Optimization in Finance

Veranstaltung: VL 4std

Dozent: Dr. Sebastian Stiller

Vorraussetzung: ADM 1&2

Synopsis:

The course is a collection of results in combinatorial optimization that are linked to applications and theory of finance. Aspects of combinatorial optimization like linear programming, graph theory, and complexity theory complement classical mathematical finance. We start with standard applications of linear programming, duality, and integer programming to arbitrage, asset pricing, construction of index funds, and option pricing. Further, we device robust optimization techniques for portfolio optimization. The second phase of the course will focus on network effects. We develop preferrential attachment models and network flow models and algorithms for clearing mechanism and default contagion. Finally, we study combinatorial models for information in markets. In particular, we study collateralized debt obligations in the light of graph theory and computational complextity. 

Literatur:

G. Cornuejols, R. Tütüncü. Optimization Methods in Finance. Cambridge 2007.

D. Easley & J. Kleinberg. Networks, Crowds, and Markets. Reasoning about a Highly Connected World. Cambridge 2010.

M. Balinski, R. Laraki. Majority Judgement - Measuring, Ranking, and Electing. MIT Press, 2010.