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Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks

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Cited by:

  1. Chen, Zhangting & Cheng, Dongya, 2024. "Precise large deviations for non-centralized sums of partial sums and random sums of heavy-tailed END random variables," Statistics & Probability Letters, Elsevier, vol. 211(C).
  2. Jaakko Lehtomaa, 2015. "Asymptotic Behaviour of Ruin Probabilities in a General Discrete Risk Model Using Moment Indices," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1380-1405, December.
  3. Li, Jinzhu, 2013. "On pairwise quasi-asymptotically independent random variables and their applications," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2081-2087.
  4. Laeven, Roger J.A. & Goovaerts, Marc J. & Hoedemakers, Tom, 2005. "Some asymptotic results for sums of dependent random variables, with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 154-172, October.
  5. Tang, Qihe & Wang, Guojing & Yuen, Kam C., 2010. "Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 362-370, April.
  6. Yang, Haizhong & Sun, Suting, 2013. "Subexponentiality of the product of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2039-2044.
  7. Eckert, Johanna & Gatzert, Nadine, 2018. "Risk- and value-based management for non-life insurers under solvency constraints," European Journal of Operational Research, Elsevier, vol. 266(2), pages 761-774.
  8. Serguei Foss & Andrew Richards, 2010. "On Sums of Conditionally Independent Subexponential Random Variables," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 102-119, February.
  9. Yang, Yang & Jiang, Tao & Wang, Kaiyong & Yuen, Kam C., 2020. "Interplay of financial and insurance risks in dependent discrete-time risk models," Statistics & Probability Letters, Elsevier, vol. 162(C).
  10. Yang, Yingying & Hu, Shuhe & Wu, Tao, 2011. "The tail probability of the product of dependent random variables from max-domains of attraction," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1876-1882.
  11. Gao Qingwu & Gu Peng & Jin Na, 2012. "Asymptotic Behavior of the Finite-Time Ruin Probability with Constant Interest Force and WUOD Heavy-Tailed Claims," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 6(1), pages 1-16, February.
  12. Mantas Dirma & Saulius Paukštys & Jonas Šiaulys, 2021. "Tails of the Moments for Sums with Dominatedly Varying Random Summands," Mathematics, MDPI, vol. 9(8), pages 1-26, April.
  13. Yuchao Dong & Jérôme Spielmann, 2020. "Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory," Post-Print hal-02170829, HAL.
  14. Yuchao Dong & Jérôme Spielmann, 2019. "Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory," Working Papers hal-02170829, HAL.
  15. Fu, Ke-Ang & Ng, Cheuk Yin Andrew, 2014. "Asymptotics for the ruin probability of a time-dependent renewal risk model with geometric Lévy process investment returns and dominatedly-varying-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 80-87.
  16. Nyrhinen, Harri, 2007. "Convex large deviation rate functions under mixtures of linear transformations, with an application to ruin theory," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 947-959, July.
  17. Dan Zhu & Ming Zhou & Chuancun Yin, 2023. "Finite-Time Ruin Probabilities of Bidimensional Risk Models with Correlated Brownian Motions," Mathematics, MDPI, vol. 11(12), pages 1-18, June.
  18. Yiqing Chen & Jiajun Liu & Yang Yang, 2023. "Ruin under Light-Tailed or Moderately Heavy-Tailed Insurance Risks Interplayed with Financial Risks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
  19. Hashorva, Enkelejd & Pakes, Anthony G. & Tang, Qihe, 2010. "Asymptotics of random contractions," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 405-414, December.
  20. Xin-mei Shen & Zheng-yan Lin & Yi Zhang, 2009. "Uniform Estimate for Maximum of Randomly Weighted Sums with Applications to Ruin Theory," Methodology and Computing in Applied Probability, Springer, vol. 11(4), pages 669-685, December.
  21. Yang Yang & Shuang Liu & Kam Chuen Yuen, 2022. "Second-Order Tail Behavior for Stochastic Discounted Value of Aggregate Net Losses in a Discrete-Time Risk Model," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2600-2621, December.
  22. Li, Jinzhu, 2016. "Uniform asymptotics for a multi-dimensional time-dependent risk model with multivariate regularly varying claims and stochastic return," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 195-204.
  23. Yang, Yang & Leipus, Remigijus & Šiaulys, Jonas, 2014. "Closure property and maximum of randomly weighted sums with heavy-tailed increments," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 162-170.
  24. Wang, Yinfeng & Yin, Chuancun, 2010. "Approximation for the ruin probabilities in a discrete time risk model with dependent risks," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1335-1342, September.
  25. Liu, Yan, 2007. "Precise large deviations for negatively associated random variables with consistently varying tails," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 181-189, January.
  26. Sun, Ying & Wei, Li, 2014. "The finite-time ruin probability with heavy-tailed and dependent insurance and financial risks," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 178-183.
  27. Dimitrios G. Konstantinides & Christos E. Kountzakis, 2017. "Distributions with Heavy Tails in Orlicz Spaces," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1726-1762, December.
  28. Kaas, Rob & Tang, Qihe, 2005. "A large deviation result for aggregate claims with dependent claim occurrences," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 251-259, June.
  29. Yiqing Chen & Kam C. Yuen & Kai W. Ng, 2011. "Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 821-833, December.
  30. Zhang, Yuanyuan & Wang, Wensheng, 2012. "Ruin probabilities of a bidimensional risk model with investment," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 130-138.
  31. Zhang, Yi & Shen, Xinmei & Weng, Chengguo, 2009. "Approximation of the tail probability of randomly weighted sums and applications," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 655-675, February.
  32. Liu, Yang & Chen, Zhenlong & Fu, Ke-Ang, 2021. "Asymptotics for a time-dependent renewal risk model with subexponential main claims and delayed claims," Statistics & Probability Letters, Elsevier, vol. 177(C).
  33. Hashorva, Enkelejd, 2010. "On the residual dependence index of elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1070-1078, July.
  34. Gao, Qingwu & Liu, Xijun, 2013. "Uniform asymptotics for the finite-time ruin probability with upper tail asymptotically independent claims and constant force of interest," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1527-1538.
  35. Tang, Qihe & Vernic, Raluca, 2007. "The impact on ruin probabilities of the association structure among financial risks," Statistics & Probability Letters, Elsevier, vol. 77(14), pages 1522-1525, August.
  36. Fu, Ke-Ang & Ng, Cheuk Yin Andrew, 2017. "Uniform asymptotics for the ruin probabilities of a two-dimensional renewal risk model with dependent claims and risky investments," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 227-235.
  37. Kaiyong Wang & Yuebao Wang & Qingwu Gao, 2013. "Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 109-124, March.
  38. Yang, Yang & Ignatavičiūtė, Eglė & Šiaulys, Jonas, 2015. "Conditional tail expectation of randomly weighted sums with heavy-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 20-28.
  39. 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.
  40. Li, Rong & Bi, Xiuchun & Zhang, Shuguang, 2020. "Large deviations for sums of claims in a general renewal risk model with the regression dependent structure," Statistics & Probability Letters, Elsevier, vol. 165(C).
  41. Bai, Xiaodong & Song, Lixin, 2012. "Asymptotic behavior of random time absolute ruin probability with D∩L tailed and conditionally independent claim sizes," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1718-1726.
  42. Chen, Yu & Zhang, Weiping, 2007. "Large deviations for random sums of negatively dependent random variables with consistently varying tails," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 530-538, March.
  43. Gao, Qingwu & Lin, Jia’nan & Liu, Xijun, 2023. "Large deviations of aggregate amount of claims in compound risk model with arbitrary dependence between claim sizes and waiting times," Statistics & Probability Letters, Elsevier, vol. 197(C).
  44. Li, Jinzhu, 2018. "On the joint tail behavior of randomly weighted sums of heavy-tailed random variables," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 40-53.
  45. Wang, Dingcheng & Chen, Pingyan & Su, Chun, 2007. "The supremum of random walk with negatively associated and heavy-tailed steps," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1403-1412, July.
  46. Jiang, Tao & Wang, Yuebao & Chen, Yang & Xu, Hui, 2015. "Uniform asymptotic estimate for finite-time ruin probabilities of a time-dependent bidimensional renewal model," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 45-53.
  47. Wang, Dingcheng & Tang, Qihe, 2004. "Maxima of sums and random sums for negatively associated random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 287-295, July.
  48. Jing Liu & Huan Zhang, 2017. "Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments," Risks, MDPI, vol. 5(2), pages 1-11, May.
  49. Dong, Y. & Spielmann, J., 2020. "Weak limits of random coefficient autoregressive processes and their application in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 1-11.
  50. Qu, Zhihui & Chen, Yu, 2013. "Approximations of the tail probability of the product of dependent extremal random variables and applications," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 169-178.
  51. Chen, Yiqing & Yuen, Kam C., 2012. "Precise large deviations of aggregate claims in a size-dependent renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 457-461.
  52. Hongmin Xiao & Lin Xie, 2018. "Asymptotic Ruin Probability of a Bidimensional Risk Model Based on Entrance Processes with Constant Interest Rate," Risks, MDPI, vol. 6(4), pages 1-12, November.
  53. Chen, Yiqing & Ng, Kai W., 2007. "The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 415-423, May.
  54. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
  55. Constantinescu, Corina & Hashorva, Enkelejd & Ji, Lanpeng, 2011. "Archimedean copulas in finite and infinite dimensions—with application to ruin problems," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 487-495.
  56. Brignone, Riccardo & Kyriakou, Ioannis & Fusai, Gianluca, 2021. "Moment-matching approximations for stochastic sums in non-Gaussian Ornstein–Uhlenbeck models," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 232-247.
  57. Fu, Ke-Ang & Liu, Yang & Wang, Jiangfeng, 2022. "Precise large deviations in a bidimensional risk model with arbitrary dependence between claim-size vectors and waiting times," Statistics & Probability Letters, Elsevier, vol. 184(C).
  58. Chen, Yiqing & Yuan, Zhongyi, 2017. "A revisit to ruin probabilities in the presence of heavy-tailed insurance and financial risks," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 75-81.
  59. Jaunė, Eglė & Šiaulys, Jonas, 2022. "Asymptotic risk decomposition for regularly varying distributions with tail dependence," Applied Mathematics and Computation, Elsevier, vol. 427(C).
  60. Albrecher, Hansjoerg & Constantinescu, Corina & Thomann, Enrique, 2012. "Asymptotic results for renewal risk models with risky investments," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3767-3789.
  61. Leipus, Remigijus & Paukštys, Saulius & Šiaulys, Jonas, 2021. "Tails of higher-order moments of sums with heavy-tailed increments and application to the Haezendonck–Goovaerts risk measure," Statistics & Probability Letters, Elsevier, vol. 170(C).
  62. Jostein Paulsen, 2008. "Ruin models with investment income," Papers 0806.4125, arXiv.org, revised Dec 2008.
  63. Chen, Yiqing, 2017. "Interplay of subexponential and dependent insurance and financial risks," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 78-83.
  64. Helena Jasiulewicz & Wojciech Kordecki, 2015. "Ruin probability of a discrete-time risk process with proportional reinsurance and investment for exponential and Pareto distributions," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 25(3), pages 17-38.
  65. Wei, Li, 2009. "Ruin probability in the presence of interest earnings and tax payments," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 133-138, August.
  66. Chen, Yiqing & Liu, Jiajun & Liu, Fei, 2015. "Ruin with insurance and financial risks following the least risky FGM dependence structure," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 98-106.
  67. Lin, Jianxi, 2019. "Second order tail approximation for the maxima of randomly weighted sums with applications to ruin theory and numerical examples," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 37-47.
  68. Chen Yu & Zhang Weiping & Liu Jie, 2010. "Asymptotic Tail Probability of Randomly Weighted Sum of Dependent Heavy-Tailed Random Variables," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 4(2), pages 1-11, July.
  69. Lee, Wing Yan & Li, Xiaolong & Liu, Fangda & Shi, Yifan & Yam, Sheung Chi Phillip, 2021. "A Fourier-cosine method for finite-time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 256-267.
  70. Yang, Yang & Leipus, Remigijus & Šiaulys, Jonas, 2012. "Tail probability of randomly weighted sums of subexponential random variables under a dependence structure," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1727-1736.
  71. Klüppelberg, Claudia & Kostadinova, Radostina, 2008. "Integrated insurance risk models with exponential Lévy investment," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 560-577, April.
  72. Yuchao Dong & J'er^ome Spielmann, 2019. "Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory," Papers 1907.01828, arXiv.org, revised Feb 2020.
  73. Saulius Paukštys & Jonas Šiaulys & Remigijus Leipus, 2023. "Truncated Moments for Heavy-Tailed and Related Distribution Classes," Mathematics, MDPI, vol. 11(9), pages 1-15, May.
  74. Chen, Yu & Su, Chun, 2006. "Finite time ruin probability with heavy-tailed insurance and financial risks," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1812-1820, October.
  75. Abouzar Bazyari, 2023. "On the Ruin Probabilities in a Discrete Time Insurance Risk Process with Capital Injections and Reinsurance," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1623-1650, August.
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