Contribution to the weak convergence of empirical copula process : contribution to the stochastic claims reserving in general insurance

Abstract : The aim of this thesis is twofold. First, we concentrate on the study of weak convergence of weighted empirical copula processes. We provide sufficient conditions for this convergence to hold to a limiting Gaussian process. Our results are obtained in the framework of convergence in the Banach space $L^{p}$ ($1\leq p <\infty $). Statistical applications to goodness of fit (GOF) tests for copulas are given to illustrate these results. We pay special attention to GOF tests based on Cramér-von Mises type statistics. Second, we discuss the problem of stochastic claims reserving in general non-life insurance. Stochastic models are needed in order to assess the variability of the claims reserve. The starting point of this thesis is an observed inconsistency between the approaches used in practice and that suggested in the literature. To fill this gap, we present a general tool for measuring the uncertainty of reserves in the framework of ultimate (Chapter 3) and one-year time horizon (Chapter 4), based on the Chain-Ladder method.
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Przemyslaw Sloma. Contribution to the weak convergence of empirical copula process : contribution to the stochastic claims reserving in general insurance. General Mathematics [math.GM]. Université Pierre et Marie Curie - Paris VI, 2014. English. ⟨NNT : 2014PA066563⟩. ⟨tel-01207497⟩

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