Risk quantification; Systemic risk on networks; Extreme value theory; Simulation; Multivariate dependence; Downscaling
Engelke Sebastian, Davison Anthony C. (2018), Optimal regionalization of extreme value distributions for flood estimation, in Journal of Hydrology
, 556, 182-193.
Dombry Clément, Engelke Sebastian, Oesting Marco (2017), Bayesian inference for multivariate extreme value distributions, in Electronic Journal of Statistics
, 11, 4813-4844.
Debicki Krzysztof, Engelke Sebastian, Hashorva Enkelejd (2017), Generalized Pickands constants and stationary max-stable processes, in Extremes
, 20, 493-517.
Engelke Sebastian, Kabluchko Zakhar (2016), A characterization of the normal distribution using stationary max-stable processes, in Extremes
, 19, 1-6.
Engelke Sebastian, Ivanovs Jevgenijs (2016), A Lévy-derived process seen from its supremum and max-stable processes, in Electronic Journal of Probability
, 21, 1-20.
Dombry Clément, Engelke Sebastian, Oesting Marco (2016), Exact simulation of max-stable processes, in Biometrika
, 106, 303-317.
Engelke Sebastian, Ivanovs Jevgenijs, Robust bounds in multivariate extremes, in Annals of Applied Probability
Extreme value theory is an important and widely-used approach to multivariate risk assessment which provides mathematically justified estimates of small tail probabilities. It is a rapidly evolving area of research at the interface of probability theory, statistical methods and applications. Both theory and statistical methods for univariate tail analysis are well-developed. While the probabilistic foundations for multivariate theory and complex events are quickly advancing, there is still much potential to translate them into effective tools and statistical models. This is crucial for an improved application of extreme value theory for risk assessment in applied science and industry. The main objective of my research project is thus to provide tools and methods that facilitate risk quantification in complex applications.The first part of this project will tackle the as yet unsolved problem of generating random samples from multivariate extreme value distributions. Even though this is regularly needed for evaluation of risk measures via Monte Carlo methods, simulation studies of statistical methods or rare event generation,only inexact and time-intensive algorithms are currently available. In the second part, the question whether the risk of extreme weather events will change in future will be addressed. Long-term climate models predict meteorological variables only on very large scales. A method that allows for downscaling of the output of these models to information on local extreme events will be developed. The third part of the project aims at opening up new fields of application for multivariate extreme value theory. Complex systems like, for instance, river networks or systems of interacting banks, can often be represented as graphical structures. New models that take the connections in these networks into account will allow for an accurate assessment of systemic risk. A workshop on risk quantification with extreme value methods and their applications in related fields will be organized withinthe scope of this independent research project.