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On the time to ruin and the deficit at ruin in a risk model with double-sided jumps

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  • Xing, Xiaoyu
  • Zhang, Wei
  • Jiang, Yiming

Abstract

In this paper, we consider a jump diffusion risk model, which consists of a Brownian motion, phase type distributed positive claims and general negative claims. The distributions of the time to ruin and the deficit at ruin will be studied by using Rouché's Theorem, martingale and matrix analysis. We derive an explicit joint Laplace transform for the time to ruin and the deficit at ruin, as well as the Laplace transform for the time to ruin. Furthermore, our results still hold even when positive claims are rationally distributed.

Suggested Citation

  • Xing, Xiaoyu & Zhang, Wei & Jiang, Yiming, 2008. "On the time to ruin and the deficit at ruin in a risk model with double-sided jumps," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2692-2699, November.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:16:p:2692-2699
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    References listed on IDEAS

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    1. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
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    Cited by:

    1. Zhang, Zhimin & Yang, Hu, 2010. "A generalized penalty function in the Sparre-Andersen risk model with two-sided jumps," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 597-607, April.
    2. Chuancun Yin & Yuzhen Wen & Zhaojun Zong & Ying Shen, 2013. "The first passage time problem for mixed-exponential jump processes with applications in insurance and finance," Papers 1302.6762, arXiv.org, revised Jun 2014.
    3. Bo, Lijun & Song, Renming & Tang, Dan & Wang, Yongjin & Yang, Xuewei, 2012. "Lévy risk model with two-sided jumps and a barrier dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 280-291.

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