083017 (M11, B10) Zur Prognostik der zukünftigen Entwicklung der Lebenserwartung in Deutschland: Schwartz F.W., Seidler A., Zeitschrift für die gesamte Versicherungswissenschaft, Volume 84, 1995, pp. 565–574

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 91 KB
• Volume: 19
• Category: Article
• ISSN: 0167-6687
• DOI: 10.1016/s0167-6687(97)81678-2

✦ Synopsis

Mathematical tools of a higher theory of recursive formulas are developed. The one-to-one correspondence between the probability generating function and the stop-loss generating function is explored and applied to derive various recursions of risk theoretical interest. It is shown that the usual two-stage nested recursion to evaluate ultimate survival probabilities can be replaced by a more direct one-stage recursive algorithm. Factorial moment based infinite series representations for the probabilities and stop-loss transform are derived, and shown useful in some cases. Finite and infinite length stop-loss recursive formulas involving first-and secondorder backward differences are obtained for a general compound distribution.