Document JFM 58.1177.05

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Esscher, F.

On the probability function in the collective theory of risk. (English) JFM 58.1177.05

Skand. Aktuarie-Tidskrift 15, 175-195 (1932).

Es werden auf einem anderen Weg einige Formeln der Lundbergschen Theorie (s. vorstehendes Referat) abgeleitet und ein Verfahren entwickelt, mit dem numerisch die Wahrscheinlichkeit, daß\^^Mdie Gesamtauszahlung kleiner als \(x\) bleibt, bei einer erwarteten Schadenanzahl \(P\) \[ F(x, P)=\sum \frac {e^{-P}\cdot P^n}{n!} w_n (x) \] und \[ w_n (x) = \int ^x_0 w_{n-1} (x-z)ds(z) \] für verschiedene Annahmen über die “Risikofunktion” \(s(z)\) berechnet wird.

Reviewer: Lorey, W., Prof. (Frankfurt am Main)

Cited in 2 Reviews

Cited in 58 Documents

JFM Section:

Zweiter Halbband. Vierter Abschnitt. Kapitel 16. Wahrscheinlichkeitsrechnung mit Anwendungen.

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