Modeling and stochastic analysis of time series and stochastic processes

In this area of research, models for time series are developed and analysed which are motivated by applications to financial data models. The paper with Rachev (1990, 1994) is among the first papers proposing and analysing an approach for option prices in non-normal times series. For determining optimal estimators in time series models it is of interest to study the closedness of subspaces (in time or spectral domain). Recent papers are concerned with option pricing in non-complete markets as well as with the problem of ordering prices for derivates. These questions are closely related with statistical problems of modeling and with the construction and characterizing of risk measures. The statistical analysis of estimation problems in models of diffusion processes and Levy processes being observed at discrete time points is another field of interest. Coworkers: Jan Bergenthum, Christian Burgert, Christian Lauer

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

Start of project: 2002
End of project: (unlimited)

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

• Döhler S, Rüschendorf L: Nonparametric estimation of regression functions in point process models. Statistical Inference for Stochastic Processes, 2003; 6 (3): 291-307.
• Döhler S, Rüschendorf L: A consistency result in general censoring models. Statistics, 2003; 37: 205-216.
• Döhler S, Rüschendorf L: On adaptive estimation by neural net type estimators. In: D. Denison, M. Hansen, C. Holmes, B. Mallick, B. Yu (Hrsg.): Nonlinear Estimation and Classification. Springer, 2003; 381-392 (Lecture Notes in Statistics, Vol. 171).
• Döhler S, Rüschendorf L: Adaptive estimation of hazard functions. Probab. Math. Stat., 2002; 22 (2): 355-379.
• Goll T, Rüschendorf L: Minimal distance martingale measures and optimal portfolios consistent with observed market prices. In: R. Buckdahn, H.J. Engelbert, M. Yor (Hrsg.): Stochastic Processes and Related Topics. Taylor & Francis, 2002; 141-154 (Stochastics Monographs).
• Rüschendorf L: On upper and lower prices in discrete time models. Proc. Steklov Math. Inst., 2002; 237: 134-139.
• Rüschendorf L, Woerner J: Expansion of transition distributions of Levy processes in small time. Bernoulli, 2002; 8 (1): 81-96. (in Druck)
• Goll T, Rüschendorf L: Minimax and minimal distance martingale measures and their relationship to portfolio optimization. Finance and Stochastics, 2001; 5 (4): 557-581.
• Höpfner R, Rüschendorf L: Comparison of estimators in stable models. Mathematical and Computer Modelling, 1999; 29: 145-160.
• Mittnik S, Rachev S T, Rüschendorf L: Test on association of multivariate stable vectors. Mathematical and Computer Modelling, 1999; 29: 181-195.
• Averkamp R.: Conditions for the completeness of the spectral domain of a harmonizable process. Stochastic Processes and Their Applications, 1997; 72 (1): 1-9.
• Rachev S.T, Rüschendorf L: Models for option pricing. Theory Probab. Applications, 1994; 39: 150-199.