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The Joint Distribution of Surplus Immediately before Ruin and the Deficit at Ruin under Interest Force

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  • Hailiang Yang
  • Lihong Zhang

Abstract

In this paper we consider a compound Poisson risk model with a constant interest force. We investigate the joint distribution of the surplus immediately before and after ruin. By adapting the techniques in Sundt and Teugels (1995), we obtain integral equations satisfied by the joint distribution function and a Lundberg-type inequality. In the case of zero initial reserve and the case of exponential claim sizes, we obtain explicit expressions for the joint distribution function.

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  • Hailiang Yang & Lihong Zhang, 2001. "The Joint Distribution of Surplus Immediately before Ruin and the Deficit at Ruin under Interest Force," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(3), pages 92-103.
    • Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:92-103
    DOI: 10.1080/10920277.2001.10596001
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    Cited by:

    1. Schmidli, Hanspeter, 2015. "Extended Gerber–Shiu functions in a risk model with interest," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 271-275.
    2. Jostein Paulsen, 2008. "Ruin models with investment income," Papers 0806.4125, arXiv.org, revised Dec 2008.
    3. Cai, Jun & Dickson, David C. M., 2002. "On the expected discounted penalty function at ruin of a surplus process with interest," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 389-404, June.
    4. Wu, Rong & Wang, Guojing & Zhang, Chunsheng, 2005. "On a joint distribution for the risk process with constant interest force," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 365-374, June.
    5. Cheng, Yebin & Tang, Qihe & Yang, Hailiang, 2002. "Approximations for moments of deficit at ruin with exponential and subexponential claims," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 367-378, October.

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