Risk Theory pp 169-181 | Cite as

Change of Measure Techniques

  • Hanspeter Schmidli
Part of the Springer Actuarial book series (SPACT)


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.

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© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of CologneCologneGermany

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