Định lượng các Cận Giới cho Tổng của các Biến Ngẫu Nhiên Thay Đổi Đều Phụ Thuộc Dưới Các Mô Hình Copula Archimedean

Arbenz P, Embrechts P, Puccetti G (2011) The AEP algorithm for the fast computation of the distribution of the sum of dependent random variables. Bernoulli 17:562–591 Asmussen S, Binswanger K (1997) Simulation of ruin probabilities for subexponential claims. ASTIN Bullet 27(2):297–318 Asmussen S, Kroese D (2006) P Improved algorithms for rare event simulation with heavy tails. Adv Appl Probab 38:545–558 Asmussen S, Glynn PM (2006) Stochastic simulation: algorithms and analysis. Stochastic Modelling and Applied Probability, vol 57. Springer, New York Asmussen S, Blanchet J, Juneja S, Rojas-Nandayapa L (2011) Efficient simulation of tail probabilities of sums of correlated lognormals. Ann Oper Res 189:5–23 Barbe P, Genest C, Ghoudi K, Rémillard B (1996) On Kendall’s process. J Multivar Anal 58(2):197–229 Blanchet J, Juneja S, Rojas-Nandayapa L (2008) Efficient tail estimation for sums of correlated lognormals. In: Mason SJ, Hill RR, Mönch L, Rose O, Jefferson T, Fowler JW (eds) Proceedings of the Winter Simulation Conference, pp 607–614 Blanchet J, Rojas-Nandayapa L (2011) Efficient simulation of tail probability of sums of dependent random variables. J Appl Probab 48A:147–164 Boots NK, Shahabuddin P (2001) Simulating ruin probabilities in insurance risk processes with subexponential claims. In: Mason SJ, Hill RR, Mönch L, Rose O, Jefferson T, Fowler JW (eds) Proceedings of the Winter Simulation Conference, pp 468–476 Brechmann EC, Hendrich K, Czado C (2013) Conditional copula simulation for systemic risk stress testing. Insur: Math Econ 53:722–732 Brechmann EC (2014) Hierarchical Kendall copulas: Properties and inference. Can J Stat 42(1):78–108 Chan JCC, Kroese DP (2010) Efficient estimation of large portfolio loss probabilities in t-copula models. Eur J Oper Res 205(2):361–367 Chan JCC, Kroese DP (2011) Rare-event probability estimation with conditional Monte-Carlo. Ann Oper Res 189(1):43–61 Charpentier A, Segers J (2009) Tails of multivariate Archimedean copulas. J Multivar Anal 100:1521–1537 Cossette H, Côté M-P, Mailhot M, Marceau E (2014) A note on the computation of sharp numerical bounds for the distribution of the sum, product or ratio of dependent risks. J Multivar Anal 130:1–20 Fang K, Fang BQ (1988) Some families of multivariate symmetric distributions related to exponential distribution. J Multivar Anal 24:109–122 Hofert M (2008) Sampling Archimedean copulas. Comput Stat Data Anal 52:5163–5174 Jessen AH, Mikosch T (2006) Regularly varying functions. Publication de l’institut mathematique Juneja S, Shahabuddin P (2002) Simulating heavy tailed processes using delayed hazard rate twisting. ACM Trans Model Comput Simul 12(2):94–118 Kimberling CH (1974) A probabilistic interpretation of complete motonocity. Aequationes Math 10:152–164 Kortschak D, Hashorva E (2013) Efficient simulation of tail probabilities for sums of log-elliptical risks. J Comput Appl Math 247:53–67 Ling CH (1965) Representation of associative functions. Publ Math Debrecen 12:189–212 Marshall AW, Olkin I (1988) Families of multivariate distributions. J Amer Stat Assoc 83(403):834–841 McNeil AJ (2008) Sampling nested Archimedean copulas. J Statist Comput Simul 78:567–581 McNeil AJ, Neslehovà J (2009) Multivariate Archimedean copulas, d-monotone functions and L 1-norm symmetric distributions. Ann Stat 37(5B):3059–3097 Sun Y, Li H (2010) Tail approximation of value-at-risk under multivariate regular variation. Unpublished Wüthrich M (2003) Asymptotic value-at-risk estimates for sum of dependent random variables. ASTIN Bullet 33(1):75–92 Yuen KC, Yin C (2012) Asymptotic results for tail probabilities of sums of dependent and heavy-tailed random variables. Chin Ann Math 33B(4):557–568