## ESF (European Science Foundation) Research Networking Project: Advanced Mathematical Methods for Finance

This project aims at the development and application of advanced mathematical tools in finance. Methods from stochastic analysis, deterministic and stochastic control theory, the theory of differential equations, functional analysis, mathematical statistics, numerical analysis and simulation, are playing an increasingly important role in the study of financial instruments and the very complex markets in which these instruments are traded. In particular, the problems associated with the pricing and hedging of derivatives, the implementation of large scale portfolio optimization methodologies, and the modeling of the dynamics of interest rates have inspired the development of sophisticated analytical tools and new mathematical methods of great importance for problems in financial economics. A good example is the novel use of Lévy processes as the basis for a more accurate description of the dynamics and statistical properties of asset prices. As a consequence of the great variety of techniques required for progress in the development of viable financial models and risk management tools, there is a serious need for a highly interdisciplinary approach to research in this area, an approach requiring expertise from a number of complementary areas of mathematics.

##### Collaborators

- H. Körezlioğlu (Coordinator), Ö. Uğur, A. Hayfavi, K. Yıldırak, Institute of Applied Mathematics, METU
- E. Gaygısız, Department of Economics & Institute of Applied Mathematics, METU
- B. Karasözen, Department of Mathematics & Institute of Applied Mathematics, METU

Funded by ESF, TÜBİTAK, Scientific and Technical Research Council of Turkey