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Lundberg Approximations for Compound Distributions with Insurance Applications. By G. E. Willmot and X. S. Lin. (Springer, 2000)

Citations

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Cited by:

  1. Diasparra, M. & Romera, R., 2010. "Inequalities for the ruin probability in a controlled discrete-time risk process," European Journal of Operational Research, Elsevier, vol. 204(3), pages 496-504, August.
  2. Landriault, David & Moutanabbir, Khouzeima & Willmot, Gordon E., 2015. "A note on order statistics in the mixed Erlang case," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 13-18.
  3. Wei, Xiao & Hu, Yijun, 2008. "Ruin probabilities for discrete time risk models with stochastic rates of interest," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 707-715, April.
  4. 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.
  5. Diasparra, Maikol & Romera, Rosario, 2009. "Inequalities for the ruin probability in a controlled discrete-time risk process," DES - Working Papers. Statistics and Econometrics. WS ws093513, Universidad Carlos III de Madrid. Departamento de Estadística.
  6. Landriault, David & Li, Bin & Loke, Sooie-Hoe & Willmot, Gordon E. & Xu, Di, 2017. "A note on the convexity of ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 1-6.
  7. Woo, Jae-Kyung & Cheung, Eric C.K., 2013. "A note on discounted compound renewal sums under dependency," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 170-179.
  8. Psarrakos, Georgios & Politis, Konstadinos, 2008. "Tail bounds for the joint distribution of the surplus prior to and at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 163-176, February.
  9. Groniowska, Agnieszka & Niemiro, Wojciech, 2005. "Controlled risk processes in discrete time: Lower and upper approximations to the optimal probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 433-440, June.
  10. 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.
  11. Woo, Jae-Kyung, 2011. "Refinements of two-sided bounds for renewal equations," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 189-196, March.
  12. Sangüesa, C., 2008. "Error bounds in approximations of random sums using gamma-type operators," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 484-491, April.
  13. Hansjörg Albrecher & Eleni Vatamidou, 2019. "Ruin Probability Approximations in Sparre Andersen Models with Completely Monotone Claims," Risks, MDPI, vol. 7(4), pages 1-14, October.
  14. 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.
  15. Psarrakos, Georgios, 2009. "A note on convolutions of compound geometric distributions," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1231-1237, May.
  16. Chadjiconstantinidis, Stathis & Xenos, Panos, 2022. "Refinements of bounds for tails of compound distributions and ruin probabilities," Applied Mathematics and Computation, Elsevier, vol. 421(C).
  17. 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.
  18. Søren Asmussen & Pierre Fiorini & Lester Lipsky & Tomasz Rolski & Robert Sheahan, 2008. "Asymptotic Behavior of Total Times for Jobs That Must Start Over if a Failure Occurs," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 932-944, November.
  19. 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.
  20. Franco Pellerey & Cristina Zucca, 2005. "Stochastic Bounds for the Sparre Andersen Process," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 225-247, June.
  21. 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.
  22. Cossette, Helene & Landriault, David & Marceau, Etienne, 2006. "Ruin probabilities in the discrete time renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 309-323, April.
  23. Cossette, Helene & Landriault, David & Marceau, Etienne, 2004. "Exact expressions and upper bound for ruin probabilities in the compound Markov binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 449-466, June.
  24. 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.
  25. Politis, Konstadinos, 2005. "Bounds for the probability and severity of ruin in the Sparre Andersen model," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 165-177, April.
  26. Sanguesa, C., 2006. "Approximations of ruin probabilities in mixed Poisson models with lattice claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 69-80, August.
  27. El Attar Abderrahim & El Hachloufi Mostafa & Guennoun Zine El Abidine, 2017. "An Inclusive Criterion For An Optimal Choice Of Reinsurance," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 1-22, December.
  28. Mathieu Emily & Pierre Casez & Olivier François, 2009. "Risk Assessment for Hospital‐Acquired Diseases: A Risk‐Theory Approach," Risk Analysis, John Wiley & Sons, vol. 29(4), pages 565-575, April.
  29. Cai, Jun & Dickson, David C.M., 2004. "Ruin probabilities with a Markov chain interest model," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 513-525, December.
  30. Chadjiconstantinidis, Stathis & Politis, Konstadinos, 2007. "Two-sided bounds for the distribution of the deficit at ruin in the renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 41-52, July.
  31. Diasparra, Maikol & Romera, Rosario, 2006. "Optimal policies for discrete time risk processes with a Markov chain investment model," DES - Working Papers. Statistics and Econometrics. WS ws062408, Universidad Carlos III de Madrid. Departamento de Estadística.
  32. Wang, Rongming & Yang, Hailiang & Wang, Hanxing, 2004. "On the distribution of surplus immediately after ruin under interest force and subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 703-714, December.
  33. Psarrakos, Georgios, 2009. "Asymptotic results for heavy-tailed distributions using defective renewal equations," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 774-779, March.
  34. Psarrakos, Georgios, 2010. "On the DFR property of the compound geometric distribution with applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 428-433, December.
  35. Sengupta, Debasis & Das, Sudipta, 2016. "Sharp bounds on DMRL and IMRL classes of life distributions with specified mean," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 101-107.
  36. Chahkandi, M. & Ganjali, M., 2009. "On some lifetime distributions with decreasing failure rate," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4433-4440, October.
  37. 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.
  38. 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.
  39. Sotirios Losidis & Konstadinos Politis & Georgios Psarrakos, 2021. "Exact Results and Bounds for the Joint Tail and Moments of the Recurrence Times in a Renewal Process," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1489-1505, December.
  40. 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.
  41. Kim, So-Yeun & Willmot, Gordon E., 2016. "On the analysis of ruin-related quantities in the delayed renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 77-85.
  42. F. G. Badía & C. Sangüesa, 2017. "Log-Convexity of Counting Processes Evaluated at a Random end of Observation Time with Applications to Queueing Models," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 647-664, June.
  43. 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.
  44. Mark Brown & Shuangning Li, 2018. "Sharp Bounds for Exponential Approximations of NWUE Distributions," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 875-896, September.
  45. 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.
  46. Hélène Cossette & Etienne Marceau & Fouad Marri, 2011. "Constant Dividend Barrier in a Risk Model with a Generalized Farlie-Gumbel-Morgenstern Copula," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 487-510, September.
  47. Chuancun Yin, 2013. "Optimal dividend problem for a generalized compound Poisson risk model," Papers 1305.1747, arXiv.org, revised Feb 2014.
  48. 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.
  49. Chin-Yuan Hu & Jheng-Ting Wang & Tsung-Lin Cheng, 2018. "A Characterization of Exponential Distribution in Risk Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 342-355, August.
  50. 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.
  51. Baumgartner, Carolin & Gruber, Lutz F. & Czado, Claudia, 2015. "Bayesian total loss estimation using shared random effects," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 194-201.
  52. 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.
  53. 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.
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