This paper was written on the invitation of the editors of this journal and is, in general, a review. Its aim is to show how the theory of probability and mathematical statistics are applied for solving problems of the insurance field. In § 2 a description of the basic probabilistic models in risk theory is given and the problems connected with the structure of the insurance payments are considered. Section 3 is devoted to income aspect of insurance activities and the sizes of the insurance payments are under consideration. Statistical aspects of insurance mathematics are considered in § 4.
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