A process with stochastic claim frequency and a linear dividend barrier

Thomas Siegl*, Robert F. Tichy

*Korrespondierende/r Autor/-in für diese Arbeit

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung

Abstract

The classical model of ruin theory is given by a Poisson claim number process with single claims Xi and constant premium flow. Gerber has generalized this model by a linear dividend barrier b+at. Whenever the free reserve of the insurance reaches the barrier, dividends are paid out in such a way that the reserve stays on the barrier. The aim of this paper is to give a generalization of this model by using the idea of Reinhard. After an exponentially distributed time, the claim frequency changes to a different level, and can change back again in the same way. This may be used e.g. in storm damage insurance. The computations lead to systems of partial integro differential equations which are solved.

Originalspracheenglisch
Seiten (von - bis)51-65
Seitenumfang15
FachzeitschriftInsurance: Mathematics and Economics
Jahrgang24
Ausgabenummer1-2
DOIs
PublikationsstatusVeröffentlicht - 31 März 1999

ASJC Scopus subject areas

  • Statistik und Wahrscheinlichkeit
  • Volkswirtschaftslehre und Ökonometrie
  • Statistik, Wahrscheinlichkeit und Ungewissheit

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