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Theses

Outils et modèles pour l'étude de quelques risques spatiaux et en réseaux : application aux extrêmes climatiques et à la contagion en finance

Abstract : This thesis aims at developing tools and models that are relevant for the study of some spatial risks and risks in networks. The thesis is divided into five chapters. The first one is a general introduction containing the state of the art related to each study as well as the main results. Chapter 2 develops a new multi-site precipitation generator. It is crucial to dispose of models able to produce statistically realistic precipitation series. Whereas previously introduced models in the literature deal with daily precipitation, we develop a hourly model. The latter involves only one equation and thus introduces dependence between occurrence and intensity; the aforementioned literature assumes that these processes are independent. Our model contains a common factor taking large scale atmospheric conditions into account and a multivariate autoregressive contagion term accounting for local propagation of rainfall. Despite its relative simplicity, this model shows an impressive ability to reproduce real intensities, lengths of dry periods as well as the spatial dependence structure. In Chapter 3, we propose an estimation method for max-stable processes, based on simulated likelihood techniques. Max-stable processes are ideally suited for the statistical modeling of spatial extremes but their inference is difficult. Indeed the multivariate density function is not available and thus standard likelihood-based estimation methods cannot be applied. Under appropriate assumptions, our estimator is efficient as both the temporal dimension and the number of simulation draws tend towards infinity. This approach by simulation can be used for many classes of max-stable processes and can provide better results than composite-based methods, especially in the case where only a few temporal observations are available and the spatial dependence is high
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Erwan Koch. Outils et modèles pour l'étude de quelques risques spatiaux et en réseaux : application aux extrêmes climatiques et à la contagion en finance. Gestion et management. Université Claude Bernard - Lyon I, 2014. Français. ⟨NNT : 2014LYO10138⟩. ⟨tel-01284995⟩

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