SGER: Statistics of Extremes, with Applications in Financial Time Series

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The proposal pursues a series of developments of new test statisticsfor tail independence and of new measures for tail dependence.Particularly, the investigator studies extreme correlationcoefficient, tail dependence measures, gamma test statistics. Theseare related to the study of statistics of multivariate extremes. Infinancial applications, the proposal will also specify new modelsfor asset pricing and extreme co-movements for market data, anddevelop new portfolio evaluation tools more sensitive to theseco-movements. A new measure for extreme co-movement is introduced.The proposal includes the development of statistical estimationmethods for max-stable processes. Procedures of how to calculateportfolio risk measures are also introduced using combined Markovprocess and max-stable process models.As all definitions used for extremal dependence depend on some limitprocedures and often concern statistical testing for parameters atthe edge of a specific parametric space, great care has to be takento obtain tests with sufficient power. The proposal is exactlyaiming at finding a solution for this. The investigator willcarefully compare and contrast new approaches with existing onesusing simulated as well as real data. The real data will come fromareas as diverse as insurance, finance, telecommunications,climatology, seismology, medicine, etc. Throughout applications indiverse fields (like above), extreme risks play an importantscientific, societal as well as (possibly) political role. Thedissemination of new statistical tools leading to a betterunderstanding of the occurrence of joint extremes is of greatimportance. This can be very well achieved at the level of newgraduate courses, publications in journals aimed at a broadenaudience and in discussion with scientists from other fields.