OekonoSys: Economical Systems
Project Topic
Stochastic processes for the modeling of economical systems and their long term behavior.
Project Description
Predicting the future behaviour of economic system is complicated due to the feedback effect of control actions and the non-linear behaviour of the systems. So far, economic models often assume linear relationships between different fundamental process (such as inflation, productivity or tax effects).
In the current project we will
- examine a general non-linear model for the evolution of an economy (this is first done in the area of asset-liability management (ALM) applied to pension funds)
- develop stochastic control approaches with non-linear features (such as catastrophe or crash effects) where we will generalize the worst-case control approach (see Korn and Steffensen (2006) below)
- generalize the evolution of the dynamics of prices (an example of this is the new dividend modeling approach for stock prices developed by Korn and Rogers) or of other fundamentals such as inflation (see the paper by Beletski and Korn (2006))
- generalize well-known stochastic control approaches such as impulse control
- study new structured products offered by banks and insurance companies that try to hedge risks from uncertain developments of fundamental processes (such as dynamic mortality (see the paper by Korn, Natcheva and Zipperer (2006))
Project Members
Project Chair
Participating Research Groups
- Financial Mathematics and Stochastic Controlling Group (Department of Mathematics)
- Sect. Financial Mathematics (Fraunhofer Institute for Industrial Mathematics (ITWM))
Scientific Personnel
- Jun.-Prof. Dr. Holger Kraft (Department of Mathematics)
- Dr. Gerald Kroisandt (Department of Mathematics)
- Dr. Christian Ewald (Univ. St. Andrews)
- M. Sc. Fin.Math. Aihua Zhang (Fraunhofer Institute for Industrial Mathematics (ITWM))
- Dipl.-Math. Frank Seifried (Department of Mathematics)
- Undergraduate Students
External Cooperation
Project Events and Achievements
- Project start: 01.10.2005 with a preliminary duration until the end of 2007
During the first phase of the project, work on ingredients for a general model framework for describing a modern economy and for economic decision making has already been done. This includes:
- Simple inflation models: valuation, hedging and optimal investment
- Worst-case control: A new characterization of a HJB-system type
- Modelling dynamic mortality evolution and valuation of longevity bonds
Workshops
- 20.-22.10.06: DGVFM-Workshop "Wissenschaft und Praktiker diskutieren aktuelle Entwicklungen in der Finanz- und Versicherungsmathematik" ("Science and industry discuss recent developments in financial and actuarial mathematics") in Kaiserslautern (Schedule and Slides, mainly in German)
Project Publications
Ralf Korn, Serkan Zeytun. In:
Proc. International Symposium on Combinatorial Optimization 2008. 2008
Ralf Korn. In:
Computational Management Science. 2008
Holger Kraft, Ralf Korn. In:
Financial Markets and Portfolio Management. 2008
Ralf Korn, Helen Kovilyanskaya. In:
International Journal of Theoretical and Applied Finance. Volume 10, Number 6, P. 967--984, 2007
Ralf Korn, Anke Wiese. Unpublished, Working paper, 2007
Aihua Zhang, Ralf Korn, Christian-Oliver Ewald. In:
Blätter der DGVFM XXVII. Volume 2, P. 239--258, 2007
Ralf Korn, M. Steffensen. In:
SIAM Journal on Control and Optimization 2007. To appear, 2007
T. Beletski, Ralf Korn. In: G. N. Gregoriou ed.,
Advances in Risk Management. Palgrave Macmillan, P. 170--190, October, 2006
Ralf Korn, K. Natcheva, J. Zipperer. In:
Blätter der DGVFM XXVII. Volume 3, P. 397--418, 2006 (in german)
