Dimension reduction techniques for functional data analysis model and approximate smooth random functions by lower dimensional objects. In many applications the focus of interest lies not only in dimension reduction but also in the dynamic behaviour of the lower dimensional objects. The most...

Option prices are a valuable source of information concerning risk assessments from investors about future financial payoffs. The information is summarized in the state price densities (SPD), the continuous counterpart (normalized by a constant) from Arrow-Debreu security prices. Under no...

Measuring dependence in a multivariate time series is tantamount to modelling its dynamic structure in space and time. In the context of a multivariate normally distributed time series, the evolution of the covariance (or correlation) matrix over time describes this dynamic. A wide variety of...

Value-at-Risk (VaR) of a portfolio is determined by the multivariate distribution of the risk factors increments. This distribution can be modelled through copulae, where the copulae parameters are not necessarily constant over time. For an exchange rate portfolio, copulae with time varying...