Über den Zerfall einer geschlossenen Aktivengesamtheit bei säkularer Änderung der Sterblichkeit

Summary

The author shows and briefly discusses the fundamental relation which consists between the „rates of changing“ of the probabilities of death of active and invalid persons if the general population mortality depends on time. A central feature of the analysis is the so-called „burden index“ — here also denoted as „degree of splitting“ (“Zerfallsgrad”) — in a closed community split up into active and invalid persons in course of time. The result of the investigations, also interpreted geometrically, is of great importance in studying alterations in the structure of communities of persons in pension and social insurance schemes when the decremental rates are functions of time.