Summary
This treatise deals with insurance-functions and Stieltjes-integrals. Special emphasis is given to the SS′-integral, which has been defined by Mrs.Schröder. In the first part the relation between the SchÄrf-Stieltjes-integrals and the SS′-integrals is shown and described by two essential formulas (1.04 and 1.05). In the following part, the author proves theorems about SS′-integrals with the help of theorems about SchÄrf-Stieltjes-integrals. Furthermore a new Steffensen-Stieltjes-integral is introduced. This integral should be able to replace the two SS′-integrals, but it cannot produce satisfactory results in practical application.
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Literaturverzeichnis
Rauhut, B., undG. Reichel: Die Theorie der Versicherungsfunktionen als Grundlage der Versicherungsmathematik. BlÄtter der Deutschen Gesellschaft für Versicherungsmathematik, Band VIII, Heft 1. Konrad Triltsch Verlag Würzburg.
SchÄrf, H.: über links-und rechtsseitige Stieltjes-Integrale und deren Anwendungen. Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker, Band 43, Heft 2, 1943.
Schröder, G.: Zu den Grundlagen der Versicherungsmathematik. BlÄtter der Deutschen Gesellschaft für Versicherungsmathematik, Band IX, Heft 2, 1969.
Steffensen, J. F.: On Stieltjes’ Integral and its applications to actuarial questions. Journal of the Institute of Actuaries, Band 63, 1932.
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Ludwig, U.F. Versicherungsfunktionen und Stieltjes-Integrale. Blätter DGVFM 9, 321–344 (1970). https://doi.org/10.1007/BF02808615
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DOI: https://doi.org/10.1007/BF02808615