A risk model with paying dividends and random environment

Bara Kim, Hwa Sung Kim, Jeongsim Kim

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


We consider a discrete time risk model where dividends are paid to insureds and the claim size has a discrete phase-type distribution, but the claim sizes vary according to an underlying Markov process called an environment process. In addition, the probability of paying the next dividend is affected by the current state of the underlying Markov process. We provide explicit expressions for the ruin probability and the deficit distribution at ruin by extracting a QBD (quasi-birth-and-death) structure in the model and then analyzing the QBD process. Numerical examples are also given.

Original languageEnglish
Pages (from-to)717-726
Number of pages10
JournalInsurance: Mathematics and Economics
Issue number2
Publication statusPublished - 2008 Apr

Bibliographical note

Funding Information:
This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment). This research was also funded by a research grant from Kwangwoon University in 2007.


  • Deficit distribution
  • Dividend
  • Environment process
  • Phase-type distribution
  • QBD (quasi-birth-and-death) process
  • Ruin probability

ASJC Scopus subject areas

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


Dive into the research topics of 'A risk model with paying dividends and random environment'. Together they form a unique fingerprint.

Cite this