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Inverting the Transforms Arising in the \(GI/M/1\) Risk Process Using Roots

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Mathematics and Computing 2013

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 91))

Abstract

We consider an insurance risk model for which the claim arrival process is a renewal process and the sizes of claims occur an exponentially distributed random variable. For this risk process, we give an explicit expression for the distribution of probability of ultimate ruin, the expected time to ruin and the distribution of deficit at the time of ruin, using Padé-Laplace method. We have derived results about ultimate ruin probability and the time to ruin in the renewal risk model from its dual queueing model. Also, we derive the bounds for the moments of recovery time. Finally, some numerical results have been presented in the form of tables which compare these results with some of the existing results available in the literature.

The second author received partial financial support from the Department of Science and Technology, New Delhi, India research grant SR/FTP/MS-003/2012. The third author’s research work was partially supported by NSERC.

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Author information

Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, 751007, India

    Gopinath Panda & A. D. Banik

  2. Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, ON, K7K 7B4, Canada

    M. L. Chaudhry

Authors
  1. Gopinath Panda
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  2. A. D. Banik
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  3. M. L. Chaudhry
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Corresponding author

Correspondence to A. D. Banik .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    Ram N. Mohapatra

  2. Dept of Computer Science & Engineering, Haldia Institute of Technology, Haldia, India

    Debasis Giri

  3. Ministry of Defence, Scientific Analysis Group, Defence Research and Development Organisation, New Delhi, Delhi, India

    P. K. Saxena

  4. Department of Mathematics, India Institute of Technology, Kharagpur, West Bengal, India

    P. D. Srivastava

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Panda, G., Banik, A.D., Chaudhry, M.L. (2014). Inverting the Transforms Arising in the \(GI/M/1\) Risk Process Using Roots. In: Mohapatra, R., Giri, D., Saxena, P., Srivastava, P. (eds) Mathematics and Computing 2013. Springer Proceedings in Mathematics & Statistics, vol 91. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1952-1_20

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