A process with stochastic claim frequency and a linear dividend barrier

Thomas Siegl*, Robert F. Tichy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)51-65
Number of pages15
JournalInsurance: Mathematics and Economics
Issue number1-2
Publication statusPublished - 31 Mar 1999


  • Dividends
  • Ruin
  • Storm damage
  • Time-nonhomogeneous process

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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