Multidimensional Ruin Theory

Specialeforsvar ved Zuzana Duroskova

Titel: Multidimensional Ruin Theory

Abstract: In this thesis we deal with the multidimensional ruin theory using the large deviation approach for light tailed distributions. We are interested in studying the probability of ruin for an insurance company operating with several lines of business. We introduce Cramér's ruin estimates in one dimension for a discrete time process and we extend this theorem into a multidimensional version. Using Cramér's theorem we establish the upper (lower) bound for the ruin probability and we show that this upper (lower) bound is determined by so-called the rate function. Furthermore, we replace a discrete-time process with continuous process in particular, by the multivariate Lévy process and we formulate a continuous version of Cramér's theorem. Next, we consider examples of discrete time-process and multivariate Lévy processes and we apply the theoretical knowledge to calculate the rate function. Then we discuss how to model the dependence using the Lévy copulas. This is followed by a simulation study. Finally, we explain by example how to employ the Lévy copula for light tailed distributions and how to calculate the rate function

Vejleder:  Jeffrey Collamore
Censor:    Mette M. Havning