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The Time Value of Ruin in a Sparre Andersen Model

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Cited by:

  1. Lin, X. Sheldon & Sendova, Kristina P., 2008. "The compound Poisson risk model with multiple thresholds," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 617-627, April.
  2. Lu, Yi & Li, Shuanming, 2009. "The Markovian regime-switching risk model with a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 296-303, April.
  3. Liu, Zaiming & Li, Manman & Ameer, Sherbaz, 2009. "Methods for estimating optimal Dickson and Waters modification dividend barrier," Economic Modelling, Elsevier, vol. 26(5), pages 886-892, September.
  4. Lin, X.Sheldon & Pavlova, Kristina P., 2006. "The compound Poisson risk model with a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 57-80, February.
  5. Li, Shuanming & Lu, Yi, 2009. "The distribution of total dividend payments in a Sparre Andersen model," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1246-1251, May.
  6. Runhuan Feng & Yasutaka Shimizu, 2013. "On a Generalization from Ruin to Default in a Lévy Insurance Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 773-802, December.
  7. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
  8. Ren, Jiandong, 2009. "A connection between the discounted and non-discounted expected penalty functions in the Sparre Andersen risk model," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 324-330, February.
  9. Lanpeng Ji & Chunsheng Zhang, 2014. "A Duality Result for the Generalized Erlang Risk Model," Risks, MDPI, vol. 2(4), pages 1-11, November.
  10. Willmot, Gordon E., 2007. "On the discounted penalty function in the renewal risk model with general interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 17-31, July.
  11. Dutang, C. & Lefèvre, C. & Loisel, S., 2013. "On an asymptotic rule A+B/u for ultimate ruin probabilities under dependence by mixing," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 774-785.
  12. Cossette, Hélène & Marceau, Etienne & Perreault, Samuel, 2015. "On two families of bivariate distributions with exponential marginals: Aggregation and capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 214-224.
  13. Olena Ragulina & Jonas Šiaulys, 2020. "Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy," Mathematics, MDPI, vol. 8(11), pages 1-35, October.
  14. Jiang, Wuyuan & Yang, Zhaojun & Li, Xinping, 2012. "The discounted penalty function with multi-layer dividend strategy in the phase-type risk model," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1358-1366.
  15. Feng, Runhuan, 2009. "On the total operating costs up to default in a renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 305-314, October.
  16. Simon Pojer & Stefan Thonhauser, 2023. "The Markovian Shot-noise Risk Model: A Numerical Method for Gerber-Shiu Functions," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
  17. Palash Ranjan Das & Tripti Chakrabarti, 2016. "On some aspects of Maximum Severity of Ruin," Metamorphosis: A Journal of Management Research, , vol. 15(2), pages 109-114, December.
  18. Ahn, Soohan & Badescu, Andrei L., 2007. "On the analysis of the Gerber-Shiu discounted penalty function for risk processes with Markovian arrivals," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 234-249, September.
  19. Jing Wang & Zbigniew Palmowski & Corina Constantinescu, 2021. "How Much We Gain by Surplus-Dependent Premiums—Asymptotic Analysis of Ruin Probability," Risks, MDPI, vol. 9(9), pages 1-17, August.
  20. Landriault, David, 2008. "Constant dividend barrier in a risk model with interclaim-dependent claim sizes," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 31-38, February.
  21. Wei Wang, 2015. "The Perturbed Sparre Andersen Model with Interest and a Threshold Dividend Strategy," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 251-283, June.
  22. Feng, Runhuan & Shimizu, Yasutaka, 2014. "Potential measures for spectrally negative Markov additive processes with applications in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 11-26.
  23. Li, Shuanming & Lu, Yi, 2005. "On the expected discounted penalty functions for two classes of risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 179-193, April.
  24. Wong, Jeff T.Y. & Cheung, Eric C.K., 2015. "On the time value of Parisian ruin in (dual) renewal risk processes with exponential jumps," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 280-290.
  25. Jin, Can & Li, Shuanming & Wu, Xueyuan, 2016. "On the occupation times in a delayed Sparre Andersen risk model with exponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 304-316.
  26. Albrecher, Hansjorg & Claramunt, M.Merce & Marmol, Maite, 2005. "On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 324-334, October.
  27. Willmot, Gordon E. & Woo, Jae-Kyung, 2010. "Surplus analysis for a class of Coxian interclaim time distributions with applications to mixed Erlang claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 32-41, February.
  28. Cheung, Eric C.K. & Wong, Jeff T.Y., 2017. "On the dual risk model with Parisian implementation delays in dividend payments," European Journal of Operational Research, Elsevier, vol. 257(1), pages 159-173.
  29. Landriault, David & Willmot, Gordon, 2008. "On the Gerber-Shiu discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 600-608, April.
  30. Albrecher, Hansjörg & Constantinescu, Corina & Pirsic, Gottlieb & Regensburger, Georg & Rosenkranz, Markus, 2010. "An algebraic operator approach to the analysis of Gerber-Shiu functions," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 42-51, February.
  31. Yue He & Reiichiro Kawai & Yasutaka Shimizu & Kazutoshi Yamazaki, 2022. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Papers 2203.10680, arXiv.org, revised Dec 2022.
  32. 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.
  33. Ambagaspitiya, Rohana S., 2009. "Ultimate ruin probability in the Sparre Andersen model with dependent claim sizes and claim occurrence times," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 464-472, June.
  34. Yi Lu, 2016. "On the Evaluation of Expected Penalties at Claim Instants That Cause Ruin in the Classical Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 237-255, March.
  35. Wuyuan Jiang & Zhaojun Yang, 2014. "The expected discounted penalty function for two classes of risk processes perturbed by diffusion with multiple thresholds," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(4), pages 479-495, August.
  36. Schmidli, Hanspeter, 2010. "On the Gerber-Shiu function and change of measure," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 3-11, February.
  37. Georgios Psarrakos, 2015. "On the Integrated Tail of the Deficit in the Renewal Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 497-513, June.
  38. Chao Xu & Yinghui Dong & Guojing Wang, 2019. "The pricing of defaultable bonds under a regime-switching jump-diffusion model with stochastic default barrier," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(9), pages 2185-2205, May.
  39. Orbán Mihálykó, Éva & Mihálykó, Csaba, 2011. "Mathematical investigation of the Gerber-Shiu function in the case of dependent inter-claim time and claim size," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 378-383, May.
  40. Hu Yang & Zhimin Zhang, 2009. "On a class of renewal risk model with random income," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 678-695, November.
  41. Deng, Chao & Zhou, Jieming & Deng, Yingchun, 2012. "The Gerber–Shiu discounted penalty function in a delayed renewal risk model with multi-layer dividend strategy," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1648-1656.
  42. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2010. "An elementary approach to discrete models of dividend strategies," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 109-116, February.
  43. S. X. Liu & J. Y. Guo, 2006. "Discrete Risk Model Revisited," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 303-313, June.
  44. Cheung, Eric C.K. & Landriault, David & Willmot, Gordon E. & Woo, Jae-Kyung, 2010. "Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 117-126, February.
  45. Cheung, Eric C.K., 2013. "Moments of discounted aggregate claim costs until ruin in a Sparre Andersen risk model with general interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 343-354.
  46. Jang, Jiwook & Dassios, Angelos & Zhao, Hongbiao, 2018. "Moments of renewal shot-noise processes and their applications," LSE Research Online Documents on Economics 87428, London School of Economics and Political Science, LSE Library.
  47. Yang, Hu & Zhang, Zhimin, 2008. "Gerber-Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 984-991, June.
  48. Cheung, Eric C.K., 2011. "A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 384-397, May.
  49. Zhou, Zhongbao & Xiao, Helu & Deng, Yingchun, 2015. "Markov-dependent risk model with multi-layer dividend strategy," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 273-286.
  50. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2013. "Valuing equity-linked death benefits in jump diffusion models," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 615-623.
  51. Willmot, Gordon E. & Woo, Jae-Kyung, 2012. "On the analysis of a general class of dependent risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 134-141.
  52. Li, Shuanming & Dickson, David C.M., 2006. "The maximum surplus before ruin in an Erlang(n) risk process and related problems," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 529-539, June.
  53. Psarrakos, Georgios, 2008. "Tail bounds for the distribution of the deficit in the renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 197-202, October.
  54. Zhimin Zhang & Hailiang Yang & Hu Yang, 2012. "On a Sparre Andersen Risk Model with Time-Dependent Claim Sizes and Jump-Diffusion Perturbation," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 973-995, December.
  55. Thampi K. K. & Jacob M. J. & Raju N., 2007. "Ruin Probabilities under Generalized Exponential Distribution," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 2(1), pages 1-12, May.
  56. Anna Castañer & M. Claramunt & Maite Mármol, 2012. "Ruin probability and time of ruin with a proportional reinsurance threshold strategy," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 614-638, October.
  57. Tang, Qihe & Wei, Li, 2010. "Asymptotic aspects of the Gerber-Shiu function in the renewal risk model using Wiener-Hopf factorization and convolution equivalence," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 19-31, February.
  58. Albrecher, Hansjorg & Boxma, Onno J., 2005. "On the discounted penalty function in a Markov-dependent risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 650-672, December.
  59. Josef Anton Strini & Stefan Thonhauser, 2020. "On Computations in Renewal Risk Models—Analytical and Statistical Aspects," Risks, MDPI, vol. 8(1), pages 1-20, March.
  60. Chadjiconstantinidis, Stathis & Papaioannou, Apostolos D., 2009. "Analysis of the Gerber-Shiu function and dividend barrier problems for a risk process with two classes of claims," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 470-484, December.
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