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Name: Fabien Baeriswyl 

Talk Title: Multivariate regular variation in marked Hawkes processes

Abstract: In this talk, we discuss the tail asymptotics of the clusters of marked Hawkes processes, that are self-exciting point processes describing situations in which points tend to cluster together. These models are notably used in insurance (e.g. to model claim arrivals in view of computing ruin probabilities), in epidemiology to model the spread of a disease or, more recently, in modelling tweets popularity (by considering the cascade of retweets) on Twitter. In particular, we emphasise how (multivariate) regular variation transfers from the immigrant and offspring processes as well as from the mark distribution to the distribution of the cluster itself, generalising a result due to Basrak, Wintenberger and Žugec (2019). We illustrate how the individual components of the process (i.e. the variables governing both the average number of children of an event and its mark) impact the model. This is a joint work (in progress) with Valérie Chavez-Demoulin and Olivier Wintenberger. 

This talk is a contributed talk at EVA 2021. View the programme here.