In this section we consider the most common claim number process: the Poisson process. It has very desirable theoretical properties. For example, one can derive its finite-dimensional distributions explicitly. The Poisson process has a long tradition in applied probability and stochastic process theory. In his 1903 thesis, Filip Lundberg already exploited it as a model for the claim number process N. Later on in the 1930s, Harald Craméer, the famous Swedish statistician and probabilist, extensively developed collective risk theory by using the total claim amount process S with arrivals Ti which are generated by a Poisson process. For historical reasons, but also since it has very attractive mathematical properties, the Poisson process plays a central role in insurance mathematics.
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© 2009 Springer-Verlag Berlin Heidelberg
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Mikosch, T. (2009). Models for the Claim Number Process. In: Non-Life Insurance Mathematics. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88233-6_2
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DOI: https://doi.org/10.1007/978-3-540-88233-6_2
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