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A Two-Sided First-Exit Problem for a Compound Poisson Process with a Random Upper Boundary

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Abstract

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.

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Authors and Affiliations

  1. Department of Statistics, University of Haifa, Haifa, 31905, Israel

    D. Perry

  2. Department of Mathematics and Computer Science, University of Osnabrück, 49069, Osnabrück, Germany

    W. Stadje

  3. Department of Mathematical Sciences, Binghamton University, Binghamton, NY, 13902-6000, USA

    S. Zacks

Authors
  1. D. Perry
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  2. W. Stadje
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  3. S. Zacks
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Correspondence to D. Perry.

Additional information

AMS 2000 Mathematics Subject Classification: Primary 60G40; Secondary 62K25, 6OJ75

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Perry, D., Stadje, W. & Zacks, S. A Two-Sided First-Exit Problem for a Compound Poisson Process with a Random Upper Boundary. Methodol Comput Appl Probab 7, 51–62 (2005). https://doi.org/10.1007/s11009-005-6654-6

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  • DOI: https://doi.org/10.1007/s11009-005-6654-6

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