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Two-Sided Exit Problems in the Ordered Risk Model

Methodology and Computing in Applied Probability volume 21, pages 539–549 (2019)Cite this article

Abstract

The insurance risk model in the presence of two horizontal absorbing barriers is considered. The lower barrier is the usual ruin barrier while the upper one corresponds to the dividend barrier. The distribution of two first-exit times of the risk process from the strip between the two horizontal lines is under study. The claim arrival process is governed by an Order Statistic Point Process (OSPP) which enables the derivation of formulas in terms of the joint distribution of the order statistics of a sample of uniform random variables.

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Acknowledgments

I am thankful to the anonymous referee for his useful comments and suggestions. I want to address special thanks to Mackenzie Wildman for helping me improving the presentation of my paper. My work was partially funded by a CAE grant of the Society of Actuaries.

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Authors and Affiliations

  1. Department of Statistics and Applied Probability, University of California, Santa Barbara, CA, USA

    Pierre-Olivier Goffard

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  1. Pierre-Olivier Goffard
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Correspondence to Pierre-Olivier Goffard.

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Goffard, PO. Two-Sided Exit Problems in the Ordered Risk Model. Methodol Comput Appl Probab 21, 539–549 (2019). https://doi.org/10.1007/s11009-017-9606-z

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  • DOI: https://doi.org/10.1007/s11009-017-9606-z

Keywords

  • Order statistic property
  • Joint distribution of order statistics
  • Finite-time ruin probabilities
  • First-exit time
  • Risk theory

Mathematics Subject Classification (2010)

  • 60G55
  • 60G40
  • 12E10