Asymptotics for ruin probabilities of a dependent delayed-claim risk model with general investment returns and diffusion

References

• N.H. Bingham, C.M. Goldie, and J.L. Teugels, Regular Variation, Vol. 27, Cambridge University Press, 1987. https://doi.org/10.1017/CBO9780511721434.
   Google Scholar
• L. Breiman, On some limit theorems similar to the Arc-Sin law, Theory Probab. Appl. 10 (1965), pp. 323–331. https://doi.org/10.1137/1110037.
   Web of Science ®Google Scholar
• J. Cai and H. Yang, Ruin in the perturbed compound Poisson risk process under interest force, Adv Appl. Probab. 37 (2005), pp. 819–835. https://doi.org/10.1017/s0001867800000495.
   Web of Science ®Google Scholar
• D.B. Cline and G. Samorodnitsky, Subexponentiality of the product of independent random variables, Stoch Process. Appl. 49 (1994), pp. 75–98. https://doi.org/10.1016/0304-4149(94)90113-9.
   Web of Science ®Google Scholar
• P. Embrechts, C. Klüppelberg, and T. Mikosch, Modelling Extremal Events: For Insurance and Finance, Springer Science & Business Media, 1997. https://doi.org/10.1007/978-3-642-33483-2.
   Google Scholar
• S. Emmer and C. Klüppelberg, Optimal portfolios when stock prices follow an exponential Lévy process, Finance Stoch. 8 (2004), pp. 17–44. https://doi.org/10.1007/s00780-003-0105-4.
   Web of Science ®Google Scholar
• Q. Gao, E. Zhang, and N. Jin, The ultimate ruin probability of a dependent delayed-claim risk model perturbed by diffusion with constant force of interest, Bull. Korean Math. Soc. 52 (2015), pp. 895–906. https://doi.org/10.4134/bkms.2015.52.3.895.
   Web of Science ®Google Scholar
• Q. Gao, J. Zhuang, and Z. Huang, Asymptotics for a delay-claim risk model with diffusion, dependence structures and constant force of interest, J. Comput Appl. Math. 353 (2019), pp. 219–231. https://doi.org/10.1016/j.cam.2018.12.036.
   Web of Science ®Google Scholar
• F. Guo and D. Wang, Finite-and infinite-time ruin probabilities with general stochastic investment return processes and bivariate upper tail independent and heavy-tailed claims, Adv Appl. Probab. 45 (2013), pp. 241–273. https://doi.org/10.1017/s0001867800006261.
   Web of Science ®Google Scholar
• F. Guo and D. Wang, Tail asymptotic for discounted aggregate claims with one-sided linear dependence and general investment return, Sci. China Math. 62 (2019), pp. 735–750. https://doi.org/10.1007/s11425-017-9167-0.
   Web of Science ®Google Scholar
• C. Heyde and D. Wang, Finite-time ruin probability with an exponential Lévy process investment return and heavy-tailed claims, Adv Appl. Probab. 41 (2009), pp. 206–224. https://doi.org/10.1239/aap/1240319582.
   Web of Science ®Google Scholar
• H. Hult and F. Lindskog, Ruin probabilities under general investments and heavy-tailed claims, Finance Stoch. 15 (2011), pp. 243–265. https://doi.org/10.1007/s00780-010-0135-7.
   Web of Science ®Google Scholar
• C. Klüppelberg and R. Kostadinova, Integrated insurance risk models with exponential Lévy investment, Insur. Math. Econ. 42 (2008), pp. 560–577. https://doi.org/10.1016/j.insmatheco.2007.06.002.
   Web of Science ®Google Scholar
• M.L.T. Lee, Properties and applications of the Sarmanov family of bivariate distributions, Commun. Stat.–Theory Methods 25 (1996), pp. 1207–1222. https://doi.org/10.1080/03610929608831759.
   Web of Science ®Google Scholar
• J. Li, On pairwise quasi-asymptotically independent random variables and their applications, Stat. Probab. Lett. 83 (2013), pp. 2081–2087. https://doi.org/10.1016/j.spl.2013.05.023.
   Web of Science ®Google Scholar
• J. Li, Asymptotic ruin probabilities for a renewal risk model with a random number of delayed claims, J. Ind. Manag. Optim. (2022). https://doi.org/10.3934/jimo.2022112.
   PubMedGoogle Scholar
• R. Liu, D. Wang, and F. Guo, The ruin probabilities of a discrete time risk model with one-sided linear claim sizes and dependent risks, Commun. Stat.–Theory Methods 47 (2018), pp. 1529–1550. https://doi.org/10.1080/03610926.2016.1202281.
   Web of Science ®Google Scholar
• Y. Liu, Z. Chen, and K.A. Fu, Asymptotics for a time-dependent renewal risk model with subexponential main claims and delayed claims, Stat. Probab. Lett. 177 (2021), Article ID 109174. https://doi.org/10.1016/j.spl.2021.109174.
   Web of Science ®Google Scholar
• H. Meng and G. Wang, On the expected discounted penalty function in a delayed-claims risk model, Acta Math. Appl. Sin., Eng. Ser. 28 (2012), pp. 215–224. https://doi.org/10.1007/s10255-012-0141-y.
   Web of Science ®Google Scholar
• J. Peng and J. Huang, Ruin probability in a one-sided linear model with constant interest rate, Stat. Probab. Lett. 80 (2010), pp. 662–669. https://doi.org/10.1016/j.spl.2009.12.024.
   Web of Science ®Google Scholar
• Q. Tang, G. Wang, and K.C. Yuen, Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model, Insur. Math. Econ. 46 (2010), pp. 362–370. https://doi.org/10.1016/j.insmatheco.2009.12.002.
   Web of Science ®Google Scholar
• D. Wang and Q. Tang, Tail probabilities of randomly weighted sums of random variables with dominated variation, Stoch. Models 22 (2006), pp. 253–272. https://doi.org/10.1080/1532634060064902.
   Web of Science ®Google Scholar
• H.R. Waters and A. Papatriandafylou, Ruin probabilities allowing for delay in claims settlement, Insur. Math. Econ. 4 (1985), pp. 113–122. https://doi.org/10.1016/0167-6687(85)90005-8.
   Web of Science ®Google Scholar
• Y. Xiao and J. Guo, The compound binomial risk model with time-correlated claims, Insur. Math. Econ. 41 (2007), pp. 124–133. https://doi.org/10.1016/j.insmatheco.2006.10.009.
   Web of Science ®Google Scholar
• Y. Yang, K.C. Yuen, and J. Liu, Asymptotics for ruin probabilities in Lévy-driven risk models with heavy tailed claims, J. Ind. Manag. Optim. 14 (2018), pp. 231–247. https://doi.org/10.3934/jimo.2017044.
   Google Scholar
• Y. Yang, X. Wang, and Z. Zhang, Finite-time ruin probability of a perturbed risk model with dependent main and delayed claims, Nonlinear Anal.: Model. Control 26 (2021), pp. 801–820. https://doi.org/10.15388/namc.2021.26.23963.
   Web of Science ®Google Scholar
• Y. Yang and Y. Wang, Tail behavior of the product of two dependent random variables with applications to risk theory, Extremes 16 (2013), pp. 55–74. https://doi.org/10.1007/s10687-012-0153-2.
   Web of Science ®Google Scholar
• K.C. Yuen, J. Guo, and K.W. Ng, On ultimate ruin in a delayed-claims risk model, J. Appl. Probab. 42 (2005), pp. 163–174. https://doi.org/10.1239/jap/1110381378.
   Web of Science ®Google Scholar
• K.C. Yuen and J. Guo, Ruin probabilities for time-correlated claims in the compound binomial model, Insur. Math. Econ. 29 (2001), pp. 47–57. https://doi.org/10.1016/S0167-6687(01)00071-3.
   Web of Science ®Google Scholar
• A. Zhang, S. Liu, and Y. Yang, Asymptotics for ultimate ruin probability in a by-claim risk model, Nonlinear Anal.: Model. Control 26 (2021), pp. 259–270. https://doi.org/10.15388/namc.2021.26.20948.
   Web of Science ®Google Scholar
• M. Zhou, K.Y. Wang, and Y.B. Wang, Estimates for the finite-time ruin probability with insurance and financial risks, Acta Math. Appl. Sin., Eng. Ser. 28 (2012), pp. 795–806. https://doi.org/10.1007/s10255-012-0189-8.
   Web of Science ®Google Scholar