The Markov Modulated Risk Model
An alternative generalisation of the classical risk model is to change the parameters of the model for an exponentially distributed time period. The environment is generated by a Markov chain in continuous time. In this way, any risk process may be approximated. It turns out that the asymptotic results on ruin probabilities obtained for the Cramér-Lundberg model can be generalised to this general model, both for small and large claim sizes.