Abstracts

Recent events like floods, hurricanes, and other environmental catastrophes have shown the importance to account for dependence between different types of risks in insurance modeling. Neglecting dependence can lead to severe underestimation of risk in a portfolio perspective. We present a realistic, yet mathematically tractable model to describe the joint behavior of multiple claim arrival processes. The processes are derived from independent Poisson processes by introducing a Lévy subordinator as common stochastic clock. The model supports simultaneous claim arrivals and captures the often observable phenomenon of overdispersion in claim count data. There is a very efficient simulation routine available and distributional properties like Laplace transform, probability mass function, and (mixed) moments can be derived in closed form. A convenient approximation for the loss in a large portfolio is given as well. Furthermore, it is studied how the model affects pricing and risk management of (re-)insurance products.