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This book is intended for everyone interested in ruin theory, especially those who wonder how analysis changes in the presence of heavy-tailed claims or risky investments. The focus is on the Cramér-Lundberg model and two of its extensions, a diffusion perturbed model and a model with risky investments. For each model, ruin probabilities are calculated for degenerately, uniformly and exponentially distributed claim sizes as well as for Pareto-distributed claim sizes. These ruin probabilities are then compared with one another. For the extended models, a pure diffusion risk reserve process is also analyzed.