Hostname: page-component-6bf8c574d5-xtvcr Total loading time: 0 Render date: 2025-02-27T01:36:08.247Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE UPPER FIRST-EXIT TIMES OF COMPOUND G/M PROCESSES

Published online by Cambridge University Press:  22 June 2005

W. Stadje  and
S. Zacks
W. Stadje
Affiliation:
Fachbereich Mathematik/Informatik, University of Osnabrück, 49069 Osnabrück, Germany, E-mail: wolfgang@mathematik.uni-osnabrueck.de
S. Zacks
Affiliation:
Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902-6000, E-mail: shelly@math.binghamton.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

For a compound process with exponential jumps at renewal times, we determine, in closed form, the density of the first time an upper linear boundary is crossed. It is shown how simple formulas for the Laplace transform and the first two moments can be directly derived from this density.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 3 , July 2005 , pp. 397 - 403
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Asmussen, S. (2000). Ruin probabilities. Advanced Series on Statistical Science and Applied Probability Vol. 2. Singapore: World Scientific.CrossRef
Borovkov, A.A. (1976). Stochastic processes in queueing theory. New York: Springer-Verlag.CrossRef
Borovkov, K. & Burq, Z. (2001). Kendall's identity for the first crossing time revisited. Electronic Communications in Probability 6: 91–94.Google Scholar
Perry, D., Stadje, W., & Zacks, S. (1999). Contributions to the theory of first-exit times for some compound processes in queueing theory. Queueing Systems 33: 369–379.Google Scholar
Perry, D., Stadje, W., & Zacks, S. (2002). Hitting and ruin probabilities for compound processes and the cycle maximum of M/G/1. Stochastic Models 18: 553–564.Google Scholar
Picard, P. & Lefèvre, C. (1994). On the first crossing of the surplus process with a given upper barrier. Insurance Mathematics and Economics 14: 163–179.Google Scholar
Picard, P. & Lefèvre, C. (1998). The moments of ruin time in the classical risk model with discrete claim size distribution. Insurance Mathematics and Economics 23: 157–172.Google Scholar
Picard, P. & Lefèvre, C. (1999). Corrigendum to: The moments of ruin time in the classical risk model with discrete claim size distribution. Insurance Mathematics and Economics 25: 105–107.Google Scholar
Picard, P. & Lefèvre, C. (2001). On the probability of (non)-ruin in infinite time. Scandinavian Actuarial Journal, 148–161.CrossRef
Stadje, W. & Zacks, S. (2003). Upper first-exit times of compound Poisson processes revisited. Probability in the Engineering and Informational Sciences 17: 459–465.Google Scholar