Geodesic
Some aspects of insurance mathematics
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 2, pp. 374-416

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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.
Keywords: insurance mathematics, risk theory, Poisson and compound Poisson models, Cox processes, the Cramér–Lundberg theorem, optional stopping theorem, piecewise deterministic Markov processes, general insurance risk model.
Mots-clés : martingales 
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P. Embrechts; C. Klüppelberg. Some aspects of insurance mathematics. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 2, pp. 374-416. http://geodesic.mathdoc.fr/item/TVP_1993_38_2_a9/