Change of Measure Techniques
The change of measure method is a strong probabilistic technique used successfully in actuarial and financial mathematics. In particular, by using an 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 model. As ruin is certain under the new measure, the method also yields an ideal possibility to simulate ruin probabilities.