Computational Analysis of the GI/G/1 Risk Process Using Roots

  • Gopinath Panda
  • A. D. Banik
  • M. L. Chaudhry
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 225)


In this paper, we analyze an insurance risk model wherein the arrival of claims and their sizes occur as renewal processes. Using the duality relation in queueing theory and roots method, we derive closed-form expressions for the ultimate ruin probability, the distribution of the deficit at the time of ruin, and the expected time to ruin in terms of the roots of the characteristic equation. Finally, some numerical computations are portrayed with the help of tables.


Risk processes Ruin probability Duality Padé approximation Time to ruin GI/G/1 queue Deficit at the time of ruin 



The third author’s research work was partially supported by NSERC, Canada.


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.School of Basic SciencesIndian Institute of Technology BhubaneswarBhubaneswarIndia
  2. 2.Department of Mathematics and Computer ScienceRoyal Military College of CanadaKingstonCanada

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