Titlebook: Risk Theory; Hanspeter Schmidli Book 2017 Springer International Publishing AG, part of Springer Nature 2017 MSC 2010 91B30 60F10 60G42 60

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Pastry

Risk Models, characteristics under proportional as well as excess of loss reinsurance. Via Panjer’s algorithm, we learn a method to calculate the distribution in a stable way. We will see how to approximate the distribution of a compound sum, and how to calculate the premia. We introduce risk measures known fro

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Credibility Theory,d value of the annual claim. But its distribution is unknown. A way to circumvent the lack of knowledge are Bayesian methods. As joint distributions are hard to obtain, one uses a linear prediction of the aggregate claims. These credibility methods are known under the name “Bühlmann model” or “Bühlm

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,The Cramér–Lundberg Model,odel is far from reality, it offers an excellent possibility to study the effect of a decision to the risk involved. We are particularly interested in ruin probabilities. We show how many characteristics of the model can be calculated, including the capital prior and immediately after ruin. We use b

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The Renewal Risk Model,ive random variables. We show that most of the results for the classical risk model can be generalised to the renewal model. The ruin probabilities are approximated in the small and in the large claims case. In the small claims case, we also find bounds for the ruin probabilities in finite time.

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The Ammeter Risk Model,in a single period. This distribution can be constructed by mixing the Poisson parameter with a Gamma distribution. We therefore choose annually a new mixing parameter for the Cramér-Lundberg model. The asymptotic results obtained for the classical risk model can then be generalised to this more gen

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Change of Measure Techniques,exponential martingale the surplus process transfers under the new measure to the same type of process. Several technical difficulties one observes under the original measure disappear. We illustrate the methods for the Cramér-Lundberg risk model, the Sparre-Andersen risk model and the Ammeter risk

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