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Stochastic Bounds for the Sparre Andersen Process

Author

Listed:
  • Franco Pellerey

    (Politecnico di Torino)

  • Cristina Zucca

    (Università degli Studi di Torino)

Abstract

In this paper we define two stochastic processes that are smaller and greater in usual stochastic order than the Sparre Andersen process. We derive, as a consequence, upper and lower bounds of its marginal distributions, and of the distributions of its first passage times above fixed thresholds. We also present a generalization of these stochastic bounds for risk processes perturbed by diffusion.

Suggested Citation

  • Franco Pellerey & Cristina Zucca, 2005. "Stochastic Bounds for the Sparre Andersen Process," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 225-247, June.
    • Handle: RePEc:spr:metcap:v:7:y:2005:i:2:d:10.1007_s11009-005-1484-0
    DOI: 10.1007/s11009-005-1484-0
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    References listed on IDEAS

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    1. Vladimir Kalashnikov, 1999. "Bounds for Ruin Probabilities in the Presence of Large Claims and their Comparison," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 116-128.
    2. Cai, Jun & Dickson, David C. M., 2003. "Upper bounds for ultimate ruin probabilities in the Sparre Andersen model with interest," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 61-71, February.
    3. Lindqvist, Bo Henry, 1988. "Association of probability measures on partially ordered spaces," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 111-132, August.
    4. Dickson, D. C. M., 2001. "Lundberg Approximations for Compound Distributions with Insurance Applications. By G. E. Willmot and X. S. Lin. (Springer, 2000)," British Actuarial Journal, Cambridge University Press, vol. 7(4), pages 690-691, October.
    5. Wang, Guojing & Wu, Rong, 2000. "Some distributions for classical risk process that is perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 15-24, February.
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