Insurance Mathematics: Stochastic Models and Mathematical Methods gives a modern overview on the topic, emphasizing stochastic modeling and related mathematical methods. Topics covered include models for individual and aggregate losses in a portfolio of risks, models for compound losses, methods for determining premium rates, and credibility theory, which is based on Bayesian statistics. Experience rated premiums are also discussed using the Buhlmann Straub model and other general models. The last part of this important monograph introduces important computational techniques and how to distinguish the methods arising from asymptotic analysis, i.e., the Laplace and saddlepoint approximation.