Generalized continuons-time ARMA processes

• Applicant: Professorin Dr. Vicky Fasen-Hartmann
• Subject Area: Mathematics
• Term: from 2006 to 2008
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 27869480

Generalized Ornstein-Uhlenbeck processes are continuous-time processes within a Levy framework having an exponentially decreasing autocorrelation function. They are applied as stochastic volatility models in finance and as risk models in insurance. Continuous-time processes are in particular appropriate models for irregularly-spaced and high-frequency data. Such models are limited in two ways. In practice, financial time series are often multivariate with dependent components. Furthermore, the correlation functions are not necessarily exponentially decreasing. The aim of this project is to develop a multivariate generalized Ornstein-Uhlenbeck model and to study the properties of this model. The multivariate generalized Ornstein-Uhlenbeck processes shall be enriched to allow for a class of flexible dependence structures resulting in the class of generalized continuous-time ARMA processes.

• DFG Programme: Research Fellowships
• International Connection: France, USA
• Hosts: Professor Dr. Jean Bertoin; Professor Dr.-Ing. Gennady Samorodnitsky