[1] |
TangQ, TsitsiashviliG. Precise estimates for the ruin probability in finite horizon in a discrete‐time model with heavy‐tailed insurance and financial risks. Stochastic Process Appl. 2003;108:299‐325. · Zbl 1075.91563 |
[2] |
GoovaertsM, KaasR, LaevenR, TangQ, VernicR. The tail probability of discounted sums of Pareto‐like losses in insurance. Scandinavian Actur J. 2005;2005(6):446‐461. · Zbl 1144.91026 |
[3] |
ChenY, YuenKC. Sums of pairwise quasi‐asymptotically independent random variables with consistent variation. Stoch Model. 2009;25:76‐89. · Zbl 1181.62011 |
[4] |
TangQ, YuanZ. Randomly weighted sums of subexponential random variables with applicaition to capital allocation. Extremes. 2014;17:467‐493. · Zbl 1328.62089 |
[5] |
TangQ, YuanZ. Random difference equations with subexponential innovations. Sci Chin Math. 2016;59(12):2411‐2426. · Zbl 1362.60064 |
[6] |
ChenY. Interplay of subexponential and dependent insurance and financial risks. Insur Math Econom. 2017;77:78‐83. · Zbl 1422.91333 |
[7] |
AsimitAV, BadescuAM, TsanakasA. Optimal risk transfers in insurance groups. Eur Actuar J. 2013;3(1):159‐190. · Zbl 1270.91028 |
[8] |
ArtznerP, DelbaenF, EberJM, HeathD. Coherent measures of risks. Math Finan. 1999;9:203‐228. · Zbl 0980.91042 |
[9] |
ZhuL, LiH. Tail distortion risk and its asymptotic analysis. Insur Math Econom. 2012;51(1):115‐121. · Zbl 1284.91283 |
[10] |
EmmerS, KratzM, TascheD. What is the best risk measure in practice? a comparison of standard measures. J Risk. 2015;18(2):31‐60. |
[11] |
AsimitAV, FurmanE, TangQ, VernicR. Asymptotic for risk capital allocations based on conditional tail expectation. Insur Math Econom. 2011;49:310‐324. · Zbl 1228.91029 |
[12] |
JoeH, LiH. Tail risk of multivariate regular variation. Methodol Comput Appl Probab. 2011;13(4):671‐693. · Zbl 1239.62060 |
[13] |
HuaL, JoeH. Second order regular variation and conditional tail expectation of multiple risks. Insur Math Econom. 2011;49(3):537‐546. · Zbl 1228.91039 |
[14] |
YangY, HashorvaE. Extremes and products of multivariate AC‐product risks. Insur Math Econom. 2013;52(2):312‐319. · Zbl 1284.60108 |
[15] |
YangY, IgnatavičiuteE, ŠiaulysJ. Conditional tail expectation of randomly weighted sums with heavy‐tailed distributions. Stat Probab Lett. 2015;105:20‐28. · Zbl 1328.60040 |
[16] |
AsimitAV, LiJ. Extremes for coherent risk measures. Insur Math Econom. 2016;71:332‐341. · Zbl 1371.91075 |
[17] |
XingG, LiX, YangS. On the asymptotics of tail conditional expectation for portfolio loss under bivariate Eyraud‐Farlie‐Gumbel‐Morgenstern copula and heavy tails. Commun Stat‐Simulat Comput. 2018. https://doi.org/10.1080/03610918.2018.1510526. · Zbl 07552783 · doi:10.1080/03610918.2018.1510526 |
[18] |
XingG, GanX. Asymptotic analysis of tail distortion risk measure under the framework of multivariate regular variation. Commun Stat‐Theory Methods. 2020;49(12):2931‐2941. https://doi.org/10.1080/03610926.2019.1584312. · Zbl 1511.62299 · doi:10.1080/03610926.2019.1584312 |
[19] |
YangY, WangK, LiuJ, ZhangZ. Asymptotics for a bidimensional risk model with two geometric Lévy price processes. J Ind Manag Optim. 2019;15(2):481‐505. · Zbl 1438.91119 |
[20] |
YangY, JiangT, WangK, YuenKC. Interplay of financial and insurance risks in dependent discrete‐time risk models. Stat Probab Lett. 2020;162:108752. · Zbl 1436.62501 |
[21] |
EmbrechtsP, KlüppelbergS, MikoschT. Extremal Events in Finance and Insurance. New York, NY: Springer‐Verlag; 1997. · Zbl 0873.62116 |
[22] |
FossS, KorshunovD, ZacharyS. An Introduction to Heavy‐tailed and Subexponential Distributions. New York, NY: Springer; 2011. · Zbl 1250.62025 |
[23] |
AsimitAV, BadescuAL. Extremes on the discounted aggregate claims in a time dependent risk model. Scand Actuar J. 2010;2010(2):93‐104. · Zbl 1224.91041 |
[24] |
SarmanovOV. Generalized normal correlation and two‐dimensional Fréchet classes. Dokl. Akad. Nauk SSSR. Russian Academy of Sciences, 1966;168(1):32‐35. · Zbl 0203.20001 |
[25] |
WeiL, YuanZ. The loss given default of a low‐default portfolio with weak contagion. Insur Math Econom. 2016;66:113‐123. · Zbl 1348.91187 |
[26] |
YangY, WangY. Tail behavior of the product of two dependent random variables with applications to risk theory. Extremes. 2013;16(1):55‐74. · Zbl 1329.62085 |
[27] |
LiJ, TangQ, WuR. Subexponential tails of discounted aggregate claims in a time‐dependent renewal risk model. Adv Appl Probab. 2010;42(4):1126‐1146. · Zbl 1205.62061 |
[28] |
LeeMT. Properties and applications of the Sarmanov family of bivariate distributions. Commun Stat‐Theory Methods. 1996;25(6):1207‐1222. · Zbl 0875.62205 |
[29] |
VernicR. On the distribution of a sum of Sarmanov distributed random variables. J Theor Probab. 2016;29(1):118‐142. · Zbl 1336.60024 |
[30] |
YangY, YuenKC, LiuJ. Asymptotics for ruin probabilities in Lévy‐driven risk models with heavy‐tailed claims. J Ind Manag Optim. 2018;14(1):231‐247. · Zbl 1412.91059 |
[31] |
BöckerK, KlüppelbergC. Multivariate models for operational risk. Quant Finan. 2010;10(8):855‐869. · Zbl 1204.91059 |
[32] |
EmbrechtsP, GoldieC. On closure and factorization properties of subexponential and related distributions. J Aust Math Soc. 1980;29:243‐256. · Zbl 0425.60011 |
[33] |
TangQ. The subexponentiality of products revisited. Extremes. 2006;9:231‐241. · Zbl 1142.60012 |
[34] |
BinghamNH, GoldieCM, TeugelsJL. Regular Variation. Cambridge, MA: Cambridge University Press; 1987. · Zbl 0617.26001 |
[35] |
YangY, WangK, LeipusR, ŠiaulysJ. A note on the max‐sum equivalence of randomly weighted sums of heavy‐tailed random variables. Nonlinear Anal Modell Control. 2013;84:519‐525. · Zbl 1396.60062 |
[36] |
NelsenRB. An Introduction to Copulas. 2nd ed.New York, NY: Springer‐Verlag; 2006. · Zbl 1152.62030 |