Credibility theory in continuous time

The subject of this work is the development of a credibility theory in continuous time. A short introduction is followed by the stochastic modelling of the adequate premium calculation in continuous time. The terms known from the discrete theory will be transferred to a continuous time setting. The definition of the individual premium as well as of the Bayes- and Credibility estimator as orthogonal projection each on a suitable subspace proves itself as indispensable. Thereupon a general Credibility model is formulated which can be considered as the continuous analogon of the generalized Hachemeister model examined in Merz (2004). Article written in German