A two-sided first-exit problem for a compound poisson process with a random upper boundary

D. Perry, Wolfgang Stadje, Shelly Zacks

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We consider the first-exit time of a compound Poisson process from a region that is bounded from below by an increasing straight line, while its upper boundary has positive jumps of i.i.d. sizes at Poisson times and increases linearly between jumps. An integral equation for the corresponding Laplace-Stieltjes transforms is derived and solved. The case of exponential jumps is treated separately. The problem has applications in queueing and risk theory.

Original languageEnglish
Pages (from-to)51-62
Number of pages12
JournalMethodology and Computing in Applied Probability
Issue number1
StatePublished - Mar 2005


  • Compound Poisson process
  • First-exit time
  • Integral equation
  • Linear boundary
  • Random boundary

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics

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