The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion

Sung Nok CHIU*, C. C. Yin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)

Abstract

The paper studies the joint distribution of the time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process that is perturbed by diffusion. We prove that the expected discounted penalty satisfies an integro-differential equation of renewal type, the solution of which can be expressed as a convolution formula. The asymptotic behaviour of the expected discounted penalty as the initial capital tends to infinity is discussed.

Original languageEnglish
Pages (from-to)59-66
Number of pages8
JournalInsurance: Mathematics and Economics
Volume33
Issue number1
DOIs
Publication statusPublished - 8 Aug 2003

Scopus Subject Areas

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

User-Defined Keywords

  • Deficit at ruin
  • Renewal equation
  • Ruin probability
  • Surplus prior to ruin
  • Surplus process
  • Time of ruin

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