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References

  • Bernard, Carole; Jiang, Xiao; Wang, Ruodu. Risk aggregation with dependence uncertainty. Insurance Math. Econom. 54 (2014), 93--108. MR3145855
  • Chaganty, N. Rao; Joe, Harry. Range of correlation matrices for dependent Bernoulli random variables. Biometrika 93 (2006), no. 1, 197--206. MR2277750
  • Distributions with given marginals and statistical modelling. Papers from the meeting held in Barcelona, July 17–20, 2000. Edited by Carles M. Cuadras, Josep Fortiana and José A. Rodriguez-Lallena. Kluwer Academic Publishers, Dordrecht, 2002. xxiv+244 pp. ISBN: 1-4020-0914-3 MR2058972
  • Advances in probability distributions with given marginals. Beyond the copulas. Papers from the Symposium on Distributions with Given Marginals held in Rome, April 1990. Edited by G. Dall'Aglio, S. Kotz and G. Salinetti. Mathematics and its Applications, 67. Kluwer Academic Publishers Group, Dordrecht, 1991. xviii+231 pp. ISBN: 0-7923-1156-6 MR1215942
  • de Haan, Laurens; Ferreira, Ana. Extreme value theory. An introduction. Springer Series in Operations Research and Financial Engineering. Springer, New York, 2006. xviii+417 pp. ISBN: 978-0-387-23946-0; 0-387-23946-4 MR2234156
  • Embrechts, Paul; Puccetti, Giovanni. Bounds for functions of multivariate risks. J. Multivariate Anal. 97 (2006), no. 2, 526--547. MR2234036
  • Embrechts, P., G. Puccetti, and L. Rüschendorf (2013). Model uncertainty and VaR aggregation. J. Bank. Financ./~ 37/(8), 2750--2764.
  • Embrechts, P., G. Puccetti, L. Rüschendorf, R. Wang, and A. Beleraj (2014). An academic response to Basel 3.5. phRisks, 2(1), 25--48.
  • Fréchet, Maurice. Sur les tableaux de corrélation dont les marges sont données. (French) Ann. Univ. Lyon. Sect. A. (3) 14, (1951). 53--77. MR0049518
  • Höffding, Wassilij. Maszstabinvariante Korrelationstheorie. (German) Schr. Math. Inst. u. Inst. Angew. Math. Univ. Berlin 5, (1940). 181--233. MR0004426
  • Joe, Harry. Multivariate models and dependence concepts. Monographs on Statistics and Applied Probability, 73. Chapman & Hall, London, 1997. xviii+399 pp. ISBN: 0-412-07331-5 MR1462613
  • Makarov, G. D. Estimates for the distribution function of the sum of two random variables with given marginal distributions. (Russian) Teor. Veroyatnost. i Primenen. 26 (1981), no. 4, 815--817. MR0636775
  • McNeil, Alexander J.; Frey, Rüdiger; Embrechts, Paul. Quantitative risk management. Concepts, techniques and tools. Princeton Series in Finance. Princeton University Press, Princeton, NJ, 2005. xvi+538 pp. ISBN: 0-691-12255-5 MR2175089
  • Nelsen, Roger B. An introduction to copulas. Second edition. Springer Series in Statistics. Springer, New York, 2006. xiv+269 pp. ISBN: 978-0387-28659-4; 0-387-28659-4 MR2197664
  • Rüschendorf, Ludger. Random variables with maximum sums. Adv. in Appl. Probab. 14 (1982), no. 3, 623--632. MR0665297
  • Rüschendorf, Ludger. Mathematical risk analysis. Dependence, risk bounds, optimal allocations and portfolios. Springer Series in Operations Research and Financial Engineering. Springer, Heidelberg, 2013. xii+408 pp. ISBN: 978-3-642-33589-1; 978-3-642-33590-7 MR3051756
  • Shaked, Moshe; Shanthikumar, J. George. Stochastic orders. Springer Series in Statistics. Springer, New York, 2007. xvi+473 pp. ISBN: 978-0-387-32915-4; 0-387-32915-3 MR2265633
  • Tchen, André H. Inequalities for distributions with given marginals. Ann. Probab. 8 (1980), no. 4, 814--827. MR0577318
  • Wang, Bin; Wang, Ruodu. The complete mixability and convex minimization problems with monotone marginal densities. J. Multivariate Anal. 102 (2011), no. 10, 1344--1360. MR2819953
  • Wang, Ruodu; Peng, Liang; Yang, Jingping. Bounds for the sum of dependent risks and worst value-at-risk with monotone marginal densities. Finance Stoch. 17 (2013), no. 2, 395--417. MR3038596
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