The expected time to ruin in a risk process with constant barrier via martingales

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Two risk models with a constant dividend barrier are considered. In the two models claims arrive according to a Poisson process. In the first model the claim size has a phase type distribution. In the second model the claim size is exponentially distributed, but the arrival rate, the mean claim size, and the premium rate are governed by a random environment, which changes according to a Markov process. Kella and Whitt [Kella, O., Whitt, W., 1992. Useful martingales for stochastic storage processes with Lévy input. J. Appl. Probability 29, 396-403] martingale is applied in the first model. Asmussen and Kella [Asmussen, S., Kella, O., 2000. A multi-dimensional martingale for Markov additive processes and its applications. Adv. Appl. Probability 32, 376-393] multi-dimensional martingale is applied in the second model. The expected time to ruin and the amount of dividends paid until ruin occurs are obtained for both models.

Original languageEnglish
Pages (from-to)216-228
Number of pages13
JournalInsurance: Mathematics and Economics
Issue number2 SPEC. ISS.
StatePublished - 18 Oct 2005

Bibliographical note

Funding Information:
I want to thank the financial support of the Zimerman Foundation for the Study of Banking and Finance. I want to thank the referee for the careful reading, and for pointing out to me the paper by Dickson and Waters (2004) .


  • Exponential distribution
  • Laplace transform
  • Lévy process
  • Markov additive process
  • Martingales
  • Phase type distribution
  • Reflected process
  • Time to ruin

ASJC Scopus subject areas

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


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