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The moments of the time of ruin, the surplus before ruin, and the deficit at ruin

Citations

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Cited by:

  1. 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.
  2. Franck Adékambi & Essodina Takouda, 2020. "Gerber–Shiu Function in a Class of Delayed and Perturbed Risk Model with Dependence," Risks, MDPI, vol. 8(1), pages 1-25, March.
  3. Li, Shuanming & Garrido, Jose, 2004. "On ruin for the Erlang(n) risk process," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 391-408, June.
  4. Lee, Wing Yan & Willmot, Gordon E., 2014. "On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 1-10.
  5. Willmot, Gordon E., 2002. "Compound geometric residual lifetime distributions and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 421-438, June.
  6. Chau, K.W. & Yam, S.C.P. & Yang, H., 2015. "Fourier-cosine method for Gerber–Shiu functions," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 170-180.
  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. Wang, Nan & Politis, Konstadinos, 2002. "Some characteristics of a surplus process in the presence of an upper barrier," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 231-241, April.
  9. Cossette, Hélène & Landriault, David & Marceau, Etienne & Moutanabbir, Khouzeima, 2012. "Analysis of the discounted sum of ascending ladder heights," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 393-401.
  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. Vaios Dermitzakis & Konstadinos Politis, 2011. "Asymptotics for the Moments of the Time to Ruin for the Compound Poisson Model Perturbed by Diffusion," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 749-761, December.
  12. Liu, Guoxin & Wang, Ying, 2008. "On the expected discounted penalty function for the continuous-time compound binomial risk model," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2446-2455, October.
  13. Michael V. Boutsikas & Konstadinos Politis, 2017. "Exit Times, Overshoot and Undershoot for a Surplus Process in the Presence of an Upper Barrier," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 75-95, March.
  14. Willmot, Gordon E., 2004. "A note on a class of delayed renewal risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 251-257, April.
  15. 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.
  16. Ren, Jiandong, 2005. "The expected value of the time of ruin and the moments of the discounted deficit at ruin in the perturbed classical risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 505-521, December.
  17. 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.
  18. Dickson, David C.M., 2012. "The joint distribution of the time to ruin and the number of claims until ruin in the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 334-337.
  19. Franck Adékambi & Essodina Takouda, 2022. "On the Discounted Penalty Function in a Perturbed Erlang Renewal Risk Model With Dependence," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 481-513, June.
  20. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
  21. Willmot, Gordon E. & Dickson, David C. M., 2003. "The Gerber-Shiu discounted penalty function in the stationary renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 403-411, July.
  22. Maite Teresa Marmol Jimenez & M. Mercedes Claramunt Bielsa, 2006. "Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier," Working Papers in Economics 157, Universitat de Barcelona. Espai de Recerca en Economia.
  23. Corina D. Constantinescu & Jorge M. Ramirez & Wei R. Zhu, 2019. "An application of fractional differential equations to risk theory," Finance and Stochastics, Springer, vol. 23(4), pages 1001-1024, October.
  24. 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.
  25. 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.
  26. Vaios Dermitzakis & Susan M. Pitts & Konstadinos Politis, 2010. "Lundberg-type Bounds and Asymptotics for the Moments of the Time to Ruin," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 155-175, March.
  27. 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.
  28. Schmidli, Hanspeter, 2010. "On the Gerber-Shiu function and change of measure," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 3-11, February.
  29. 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.
  30. 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.
  31. Philipp Lukas Strietzel & Anita Behme, 2022. "Moments of the Ruin Time in a Lévy Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3075-3099, December.
  32. Chi, Yichun & Jaimungal, Sebastian & Lin, X. Sheldon, 2010. "An insurance risk model with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 52-66, February.
  33. 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.
  34. Lin, X. Sheldon & Wang, Tao, 2009. "Pricing perpetual American catastrophe put options: A penalty function approach," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 287-295, April.
  35. Li, Shuanming & Garrido, José, 2002. "On the time value of ruin in the discrete time risk model," DEE - Working Papers. Business Economics. WB wb021812, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
  36. 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.
  37. Li, Shuanming & Lu, Yi, 2017. "Distributional study of finite-time ruin related problems for the classical risk model," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 319-330.
  38. Dickson, David C. M. & Hipp, Christian, 2001. "On the time to ruin for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 333-344, December.
  39. Drekic, Steve & Stafford, James E. & Willmot, Gordon E., 2004. "Symbolic calculation of the moments of the time of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 109-120, February.
  40. Qiu, Ming & Jin, Zhuo & Li, Shuanming, 2023. "Optimal risk sharing and dividend strategies under default contagion: A semi-analytical approach," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 1-23.
  41. Chi, Yichun, 2010. "Analysis of the expected discounted penalty function for a general jump-diffusion risk model and applications in finance," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 385-396, April.
  42. Jeon, Yongho & Kim, Joseph H.T., 2013. "A gamma kernel density estimation for insurance loss data," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 569-579.
  43. Tsai, Cary Chi-Liang & Willmot, Gordon E., 2002. "On the moments of the surplus process perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 327-350, December.
  44. Pitts, Susan M. & Politis, Konstadinos, 2008. "Approximations for the moments of ruin time in the compound Poisson model," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 668-679, April.
  45. Egidio dos Reis, Alfredo D., 2000. "On the moments of ruin and recovery times," Insurance: Mathematics and Economics, Elsevier, vol. 27(3), pages 331-343, December.
  46. Li, Jingchao & Dickson, David C.M. & Li, Shuanming, 2015. "Some ruin problems for the MAP risk model," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 1-8.
  47. 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.
  48. Egidio dos Reis, Alfredo D., 2002. "How many claims does it take to get ruined and recovered?," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 235-248, October.
  49. 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.
  50. Jiechang Ruan & Wenguang Yu & Ke Song & Yihan Sun & Yujuan Huang & Xinliang Yu, 2019. "A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model," Mathematics, MDPI, vol. 7(10), pages 1-12, September.
  51. 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.
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