One major task will be the development of appropriate statistical methodology for multivariate multifractal models. We will investigate the behavior of various extensions and explore the use of multifractal models for risk management and portfolio management. Further research includes the analysis of the role of innovations vis-à-vis the intrinsic volatility dynamics as well as the adaptation of the multifractal model to measures of realized volatility. Given the evidence on multi-scaling of many physical time series, we also expect that the methodological innovations in financial applications will generate spill over effects to the application of multifractal models in the natural science (for example, improved forecasts of precipitation).