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Two-Sided Exit Problems in the Ordered Risk Model

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  • Pierre-Olivier Goffard

    (University of California)

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.

Suggested Citation

  • Pierre-Olivier Goffard, 2019. "Two-Sided Exit Problems in the Ordered Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 539-549, June.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:2:d:10.1007_s11009-017-9606-z
    DOI: 10.1007/s11009-017-9606-z
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    References listed on IDEAS

    as
    1. Dimitrina S. Dimitrova & Zvetan G. Ignatov & Vladimir K. Kaishev, 2017. "On the First Crossing of Two Boundaries by an Order Statistics Risk Process," Risks, MDPI, vol. 5(3), pages 1-14, August.
    2. Rulliere, Didier & Loisel, Stephane, 2005. "The win-first probability under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 421-442, December.
    3. Claude Lefèvre & Philippe Picard, 2014. "Ruin Probabilities for Risk Models with Ordered Claim Arrivals," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 885-905, December.
    4. De Vylder, F. E. & Goovaerts, M. J., 1999. "Inequality extensions of Prabhu's formula in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 249-271, May.
    5. Dimitrova, Dimitrina S. & Kaishev, Vladimir K. & Zhao, Shouqi, 2016. "On the evaluation of finite-time ruin probabilities in a dependent risk model," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 268-286.
    6. Benjamin Avanzi, 2009. "Strategies for Dividend Distribution: A Review," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 217-251.
    7. Picard, Philippe & Lefevre, Claude, 1994. "On the first crossing of the surplus process with a given upper barrier," Insurance: Mathematics and Economics, Elsevier, vol. 14(2), pages 163-179, May.
    8. Borovkov, Konstantin A. & Dickson, David C.M., 2008. "On the ruin time distribution for a Sparre Andersen process with exponential claim sizes," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1104-1108, June.
    9. D. Perry & W. Stadje & S. Zacks, 2005. "A Two-Sided First-Exit Problem for a Compound Poisson Process with a Random Upper Boundary," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 51-62, March.
    10. Lefèvre, Claude & Picard, Philippe, 2011. "A new look at the homogeneous risk model," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 512-519.
    11. De Vylder, F. & Goovaerts, M., 2000. "Homogeneous risk models with equalized claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 223-238, May.
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