Advanced Mathematical Methods for Finance

04.04.2005 - 03.04.2010

Forschungsförderungsprojekt

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. The proposed project has two main overall goals. The first is the creation and reinforcement of relationships among European research teams in the fields of stochastic analysis, control theory, differential equations, and other relevant mathematical disciplines, with the purpose of undertaking and carrying out highly innovative interdisciplinary and interactive research in mathematical finance and its applications. The second is the cultivation and maintenance of strong and mutually reinforcing links with the financial services industry in the broadest sense, with a view to further enhancing the impact and influence of mathematical research on the financial industry. The existence of many well established research groups in Europe, all recognised centres of excellence, with many different domains of expertise, augurs well for the success of such a proposal scheme of collaboration. The presence of fifteen countries, and research groups led by many of the best international experts in the field, offers the opportunity within the scope of this proposal for (a) a very significant uplift in the overall level and visibility of European research, and (b) an effective and scientific response and way forward for addressing the many new European financial challenges.

Personen

Projektleiter_in

Uwe Schmock (E105)

Projektmitarbeiter_innen

Walter Schachermayer (E105)

Institut

E105 - Institute of Statistics and Mathematical Methods in Economics

Grant funds

European Commission (EU) Other EU Research Initiative European Commission

Schlagwörter

Deutsch	Englisch
Lévy-Prozesse	Lévy processes
Finanzmathematik und ihre Anwendungen	mathematical finance and its applications
Stochastische Analysis und Kontrolle	Stochastic analysis and control
Integro-Differential-Gleichungen	Integro-differential equations
Numerische Methoden	Numerical Methods
Kreditrisikomodelle	credit risk models
Kreditrisikoaggretation	credit risk aggregation
CreditRisk+	CreditRisk+
Bernoulli-Mischmodelle	Bernoulli mixture models
Dirichlet-Mischmodelle	Dirichlet mixture models
Approximationsgüte	approximation quality
Risikoteilung	risk sharing

Externe Partner_innen

Korteweg-de Vries Institute for Mathematics Universiteit van Amsterdam
Department of probability Theory and Matematics of Finance, Institute of Mathematics of the Polish Academy of Sciences
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées, Université de Marne la Vallée
Institute of Mathematics, Helsinki Univ. of Technology mailing address: Box 1100 FI-02015 Helsinki Univ. of Technology Finland
Department of Mathematics, Imperial College London
Istituto per le Applicazioni del Calcolo "Mauro Picone"
College of Management, Sabanci University
Center of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo
Technische Universität München,Zentrum Mathematik, Lehrstuhl für Mathematische Statistik
Department of Applied Mathematics and Computer Science, Gent University
Seminar of Applied Mathematics, ETH Zentrum
Uppsala University, Department of Mathematics
Department of Mathematical Sciences University of Aarhus
Department of Mathematics, King's College
Institute of Mathematics, Romanian Academy

Publikationen

Publikationsliste