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The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion

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  • Chiu, S. N.
  • Yin, C. C.

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  • Chiu, S. N. & Yin, C. C., 2003. "The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 59-66, August.
    • Handle: RePEc:eee:insuma:v:33:y:2003:i:1:p:59-66
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    References listed on IDEAS

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    1. Schmidli, Hanspeter, 1999. "On the Distribution of the Surplus Prior and at Ruin," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 227-244, November.
    2. Lin, X. Sheldon & Willmot, Gordon E., 1999. "Analysis of a defective renewal equation arising in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 63-84, September.
    3. Gerber, Hans U. & Shiu, Elias S. W., 1999. "From ruin theory to pricing reset guarantees and perpetual put options," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 3-14, March.
    4. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    5. Lin, X. Sheldon & Willmot, Gordon E., 2000. "The moments of the time of ruin, the surplus before ruin, and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 19-44, August.
    6. Dufresne, Francois & Gerber, Hans U., 1988. "The surpluses immediately before and at ruin, and the amount of the claim causing ruin," Insurance: Mathematics and Economics, Elsevier, vol. 7(3), pages 193-199, October.
    7. 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.
    8. Gerber, Hans U. & Landry, Bruno, 1998. "On the discounted penalty at ruin in a jump-diffusion and the perpetual put option," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 263-276, July.
    9. Dickson, David C. M. & dos Reis, Alfredo Egidio, 1994. "Ruin problems and dual events," Insurance: Mathematics and Economics, Elsevier, vol. 14(1), pages 51-60, April.
    10. Dufresne, Francois & Gerber, Hans U., 1991. "Risk theory for the compound Poisson process that is perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 51-59, March.
    11. Tsai, Cary Chi-Liang & Willmot, Gordon E., 2002. "A generalized defective renewal equation for the surplus process perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 30(1), pages 51-66, February.
    12. Veraverbeke, Noel, 1993. "Asymptotic estimates for the probability of ruin in a Poisson model with diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 13(1), pages 57-62, September.
    13. Gerber, Hans U. & Shiu, Elias S. W., 1997. "The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 129-137, November.
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    Cited by:

    1. Jos'e Miguel Flores-Contr'o, 2024. "The Gerber-Shiu Expected Discounted Penalty Function: An Application to Poverty Trapping," Papers 2402.11715, arXiv.org, revised Sep 2024.
    2. Zhou, Xiaowen, 2004. "When does surplus reach a certain level before ruin?," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 553-561, December.
    3. Wang, Guojing & Wu, Rong, 2008. "The expected discounted penalty function for the perturbed compound Poisson risk process with constant interest," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 59-64, February.
    4. Christophette Blanchet-Scalliet & Diana Dorobantu & Didier Rullière, 2013. "The density of the ruin time for a renewal-reward process perturbed by a diffusion," Post-Print hal-00625099, HAL.
    5. Chuancun Yin & Chunwei Wang, 2010. "The Perturbed Compound Poisson Risk Process with Investment and Debit Interest," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 391-413, September.
    6. Kam C. Yuen & Yuhua Lu & Rong Wu, 2009. "The compound Poisson process perturbed by a diffusion with a threshold dividend strategy," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(1), pages 73-93, January.
    7. Wan, Ning, 2007. "Dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 509-523, May.
    8. Hüsler, Jürg & Piterbarg, Vladimir, 2008. "A limit theorem for the time of ruin in a Gaussian ruin problem," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 2014-2021, November.
    9. Lu, Zhaoyang & Xu, Wei & Zhang, Yan & Sun, Yingling, 2009. "On the ruin probability for the Cox correlated risk model perturbed by diffusion," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 381-389, February.
    10. Hüsler, Jürg & Zhang, Yueming, 2008. "On first and last ruin times of Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1230-1235, August.
    11. Wang, Wenyuan & Ming, Ruixing & Hu, Yijun, 2011. "On the expected discounted penalty function for risk process with tax," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 489-501, April.

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