The aim of every insurance is to spread the risks over a collective (which should be as homogeneous as possible). From the policyholder's point of view, the applied premium for inclusion in the collective may neither be too high nor too low. On the one hand, the economic benefit of the individual is diminished with increasing premiums and, on the other hand, the probability of ruin of the collective increases with decreasing premiums when losses due to case claims occur. The lecture will first address the question of how an insurer can put together suitable collectives. Subsequently, different models in the context of premiums and ruin probabilities will be discussed.


  1. Schmidt: Versicherungsmathematik. current edition. Springer, Berlin et al.