Ruin estimation in multivariate models with Clayton dependence structure

We consider the estimation of the ruin probability in a linear portfolio of insurance risk processes. We model the total claim amount of different business activities by compound Poisson processes. We allow for dependence of the components, which we model by a Lévy copula. We study in detail a Clayton-Pareto model as representative for a large claims model and a Clayton-exponential model as a small claims model. We compare the ruin probability in the Clayton dependence model with the corresponding independent and completely dependent models.