Tools and models for studying some spatial and networked risks: application to climate extremes and contagion in finance.

Summary This thesis aims at developing tools and models adapted to the study of certain spatial and networked risks. It is divided into five chapters. The first one consists in a general introduction, containing the state of the art within which the various works are included, as well as the main results obtained. Chapter 2 proposes a new multi-site precipitation generator. It is important to have models capable of producing statistically realistic precipitation series. While the models previously introduced in the literature are mainly concerned with daily precipitation, we develop an hourly model. It involves only one equation and thus introduces a dependence between occurrence and intensity, processes often considered as independent in the literature. It includes a common factor taking into account the large-scale atmospheric conditions and a multivariate autoregressive spillover term, representing the local rainfall propagation. In spite of its relative simplicity, this model reproduces very well the intensities, the durations of drought as well as the spatial dependence in the case of Northern Brittany. In Chapter 3, we propose a method for estimating max-stable processes, based on simulated likelihood techniques. Max-stable processes are very well suited to the statistical modelling of spatial extremes, but their estimation is delicate. Indeed, the multivariate density does not have an explicit form and standard estimation methods related to the likelihood cannot be applied. Under appropriate assumptions, our estimator is efficient when the number of temporal observations and the number of simulations tend to infinity. This simulation approach can be used for many classes of max-stable processes and can provide better results than current methods using composite likelihood, especially in the case where only a few time observations are available and the spatial dependence is important.