Modeling and stochastic analysis of time series

In this area of research, models for time series are developed and analysed which are motivated by applications in financial data models and in speach recognition problems. The papers with Rachev (1990, 1994) are one of the first papers proposing and analysing an approach for the building of option prices in non-normal times series. For determining optimal estimators in time series models it is interesting to study the closedness of subspaces (in time or spectral domain). The statistical analysis, the determination of the dependency structure, and the model parameters are useful for developing stable models in financial datas. Furthermore, the consistency characteristics and the asymptotic distribution of wavelet estimators and of neural net estimators are determined. For observations which can be modeled by point processes, characteristics of neural net estimators are inspected. Applications to survival data are of special interest. The statistical analysis of estimation problems in models of diffusion processes and Levy processes being watched at discrete time points is another field of interest. Here, the motivation is the analysis of processes being developed for the description of financial data. Some of our main fields are: a) models and statistical analysis of time series with applications to financial data, b) option pricing and utility approach to optimal portfolios, c) statistical analysis of diffusion and Levy processes with application to financial models, d) wavelet estimation method and neural net estimation with application to survivial analysis and pattern recognition, e) optimal stopping problems in point processes. Staff members: Roland Averkamp, Sebastian Döhler, Thomas Goll, Jeannette Woerner

Phone: 0761/203-5665
Email: ruschen@stochastik.uni-freiburg.de

Start of project: 1994
End of project: 2001

Albert-Ludwigs-University Freiburg
Prof. Dr. Ludger Rüschendorf
Abteilung für Mathematische Stochastik
Prof. Dr. Ludger Rüschendorf
Ernst-Zermelo-Straße 1
79104 Freiburg
Germany

Phone: 0761/203-5664
Fax: 0761/203-5661
Email: sekretariat@stochastik.uni-freiburg.de
http://www.stochastik.uni-freiburg.de/rueschendorf
Actual Research Report

Optionspreise, wavelet und neuronale Netzschätzer, diskret b

• Mittnik S, Rachev S T, Rüschendorf L: Test on association of multivariate stable vectors. Mathematical and Computer Modelling, 1999; 29: 181-195.
• Kallsen J.: Semimartingale Modelling in Finance. Dissertation Universität Freiburg, 1998.
• Averkamp R.: Conditions for the completeness of the spectral domain of a harmonizable process. Stochastic Processes and Their Applications, 1997; 72 (1): 1-9.
• Michalek J, Rüschendorf L: A remark on the spectral domain of nonstationary processes. Stochastic Processes Applications, 1994; 53: 55-64.
• Rachev S.T, Rüschendorf L: Models for option pricing. Theory Probab. Applications, 1994; 39: 150-199.