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Dependence and extreme events in ruin theory : univariate and multivariate study, optimal allocation problems

Abstract : This PhD thesis presents new models and new results in ruin theory, in the case where claim amounts are heavy-tailed distributed. Classical assumptions like independence and stationarity and univariate analysis are sometimes too restrictive to describe the complex evolution of the reserves of an insurance company. In a dependence context, asymptotics of univariate finite-time ruin probability are computed. This dependence, and the other model parameters are modulated by a Markovian environment process to take into account possible correlation crisis. Then, we introduce some models which describe dependence between claim amounts and claim interarrival times we can find in earthquake or flooding risks. In multivariate framework, we present some risk criteria like multivariate ruin probability or the expectation of the timeintegrated negative part of the risk process. We solve some problems of optimal allocation for these risk measures. Then, we study the impact of the risk dangerousness and of the dependence between lines on this optimal allocation.
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Submitted on : Thursday, November 25, 2010 - 2:23:07 PM
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Romain Biard. Dependence and extreme events in ruin theory : univariate and multivariate study, optimal allocation problems. General Mathematics [math.GM]. Université Claude Bernard - Lyon I, 2010. English. ⟨NNT : 2010LYO10182⟩. ⟨tel-00539886⟩

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