A Journey from Statistics and Probability to Risk Theory An interview with Ludger Rüschendorf

Fabrizio Durante; Giovanni Puccetti; Matthias Scherer

Dependence Modeling (2015)

  • Volume: 3, Issue: 1, page 182-195, electronic only
  • ISSN: 2300-2298

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Fabrizio Durante, Giovanni Puccetti, and Matthias Scherer. "A Journey from Statistics and Probability to Risk Theory An interview with Ludger Rüschendorf." Dependence Modeling 3.1 (2015): 182-195, electronic only. <http://eudml.org/doc/275922>.

@article{FabrizioDurante2015,
author = {Fabrizio Durante, Giovanni Puccetti, Matthias Scherer},
journal = {Dependence Modeling},
language = {eng},
number = {1},
pages = {182-195, electronic only},
title = {A Journey from Statistics and Probability to Risk Theory An interview with Ludger Rüschendorf},
url = {http://eudml.org/doc/275922},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Fabrizio Durante
AU - Giovanni Puccetti
AU - Matthias Scherer
TI - A Journey from Statistics and Probability to Risk Theory An interview with Ludger Rüschendorf
JO - Dependence Modeling
PY - 2015
VL - 3
IS - 1
SP - 182
EP - 195, electronic only
LA - eng
UR - http://eudml.org/doc/275922
ER -

References

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  1. [1] Andersen, P. K., O. Borgan, R. D. Gill, and N. Keiding (2012). Statistical Models Based on Counting Processes. Springer- Verlag, New York. Zbl0769.62061
  2. [2] Bickel, P. J., Y. Ritov, and J. A. Wellner (1991). Efficient estimation of linear functionals of a probability measure P with known marginal distributions. Ann. Statist. 19(3), 1316–1346. [Crossref] Zbl0742.62034
  3. [3] Brenier, Y. (1991). Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl. Math. 44(4), 375–417. Zbl0738.46011
  4. [4] Bruss, F. T. and L. Rüschendorf (2010). On the perception of time. Gerontology 56(4), 361–370. [Crossref] 
  5. [5] Dall’Aglio, G., S. Kotz, and G. Salinetti (Eds.) (1991). Advances in Probability Distributions with Given Marginals. Kluwer Academic Publishers Group, Dordrecht. 
  6. [6] Deheuvels, P. (1979). La fonction de dépendance empirique et ses propriétés. Un test non paramétrique d’indépendance. Acad. Roy. Belg. Bull. Cl. Sci.(5) 65(6), 274–292. Zbl0422.62037
  7. [7] Deming, W. E. and F. F. Stephan (1940). On a least squares adjustment of a sampled frequency table when the expected marginal totals are known. Ann. Math. Stat. 11(4), 427–444. [Crossref] Zbl0024.05502
  8. [8] Döhler, S. and L. Rüschendorf (2003). Nonparametric estimation of regression functions in point process models. Stat. Inference Stoch. Process. 6(3), 291–307. Zbl1031.62032
  9. [9] Durante, F. and C. Sempi (2010). Copula theory: an introduction. In Copula Theory and Its Applications, Volume 198 of Lecture Notes in Statistics, pp. 3–31. Springer, Berlin. 
  10. [10] Embrechts, P. and G. Puccetti (2006). Bounds for functions of dependent risks. Finance Stoch. 10(3), 341–352. Zbl1101.60010
  11. [11] Embrechts, P., G. Puccetti, and L. Rüschendorf (2013). Model uncertainty and VaR aggregation. J. Bank. Financ. 37(8), 2750– 2764. [WoS][Crossref] 
  12. [12] Fermanian, J.-D., D. Radulovic, M. Wegkamp (2004). Weak convergence of empirical copula processes. Bernoulli 10(5), 847–860. [Crossref] Zbl1068.62059
  13. [13] Genest, C., J.-F. Quessy, B. Rémillard (2007). Asymptotic local efficiency of Cramér-von Mises tests for multivariate independence. Ann. Statist. 35(1), 166–191. [Crossref] Zbl1114.62058
  14. [14] Goll, T. and L. Rüschendorf (2001). Minimax and minimal distance martingale measures and their relationship to portfolio optimization. Finance Stoch. 5(4), 557–581. Zbl0997.91022
  15. [15] Gray, L. and D. Wilson (1980). Nonnegative factorization of positive semidefinite nonnegative matrices. Linear Algebra Appl. 31, 119 – 127. Zbl0434.15012
  16. [16] Grenander, U. (1968). Probabilities on Algebraic Structures (2nd edition). Almqvist & Wiksell, Stockholm and John Wiley, New York. Zbl0131.34804
  17. [17] Hall, P. (1935). On representatives of subsets. J. London Math. Soc. s1-10(1), 26–30. Zbl0010.34503
  18. [18] Hardy, G. H., J. E. Littlewood, and G. Pólya (1952). Inequalities (2nd edition). Cambridge University Press, Camdridge. Zbl0047.05302
  19. [19] Holtrode, R. and L. Rüschendorf (1993). Differentiablity of point process models and asymptotic efficiency of differentiable functionals. Statistics 24(1), 17–42. [Crossref] Zbl0808.62076
  20. [20] Iosifescu, M. and P. Tautu (1973). Stochastic Processes and Applications in Biology and Medicine. Springer-Verlag, Berlin- New York. Zbl0262.92002
  21. [21] Karlin, S. and J. McGregor (1964). Direct product branching processes and related Markov chains. Proc. Nat. Acad. Sci. U.S.A. 51, 598–602. [Crossref] Zbl0129.30504
  22. [22] Kellerer, H. G. (1984). Duality theorems for marginal problems. Z. Wahrsch. Verw. Gebiete 67(4), 399–432. [Crossref] Zbl0535.60002
  23. [23] Kolmogorov, A. N. (1957). On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition. Dokl. Akad. Nauk SSSR 114, 953–956. Zbl0090.27103
  24. [24] Linnik, Y. V. (1975). Problems of Analytical Statistics. Statistical Publishing Society, Calcutta. 
  25. [25] Mainik, G., G. Mitov, and L. Rüschendorf (2015). Portfolio optimization for heavy-tailed assets: Extreme risk index vs. Markowitz. J. Empirical Finance 32, 115–134. 
  26. [26] Mainik, G. and L. Rüschendorf (2010). Onoptimal portfolio diversificationwith respect to extreme risks. Finance Stoch. 14(4), 593–623. Zbl1226.91069
  27. [27] Moore, D. S. and M. C. Spruill (1975). Unified large-sample theory of general chi-squared statistics for tests of fit. Ann. Statist. 3, 599–616. Zbl0322.62047
  28. [28] Pitt, L. D. (1982). Positively correlated normal variables are associated. Ann. Probab. 10, 496–499. [Crossref] Zbl0482.62046
  29. [29] Puccetti, G. and L. Rüschendorf (2012). Computation of sharp bounds on the distribution of a function of dependent risks. J. Comput. Appl. Math. 236(7), 1833–1840. [WoS][Crossref] Zbl1241.65019
  30. [30] Rachev, S. T. and L. Rüschendorf (1998). Mass Transportation Problems. Vol. I–II. Springer, New York. Zbl0990.60500
  31. [31] Rüschendorf, L. (1976). Asymptotic distributions of multivariate rank order statistics. Ann. Statist. 4, 912–923. [Crossref] Zbl0359.62040
  32. [32] Rüschendorf, L. (1981a). Sharpness of Fréchet bounds. Z. Wahrsch. Verw. Gebiete 57(2), 293–302. [Crossref] Zbl0445.60002
  33. [33] Rüschendorf, L. (1981b). Stochastically ordered distributions and monotonicity of the OC-function of sequential probability ratio tests. Math. Operationsforsch. Statist. Ser. Statist. 12(3), 327–338. Zbl0481.62063
  34. [34] Rüschendorf, L. (1982). Random variables with maximum sums. Adv. Appl. Probab. 14, 623–632. [Crossref] Zbl0487.60026
  35. [35] Rüschendorf, L. (1991). Fréchet-bounds and their applications. In Advances in Probability Distributions with Given Marginals, Volume 67, pp. 151–187. Dordrecht: Kluwer Acad. Publ. Zbl0744.60005
  36. [36] Rüschendorf, L. (1995). Convergence of the iterative proportional fitting procedure. Ann. Statist. 23, 1160–1174. [Crossref] Zbl0851.62038
  37. [37] Rüschendorf, L. (2013). Mathematical Risk Analysis. Dependence, Risk Bounds, Optimal Allocations and Portfolios. Springer, Heidelberg. Zbl1266.91001
  38. [38] Rüschendorf, L. (2014). Mathematische Statistik. Springer, Berlin. 
  39. [39] Rüschendorf, L. and S. T. Rachev (1990). A characterization of random variables with minimum L2-distance. J. Multivariate Anal. 32(1), 48–54. [Crossref] Zbl0688.62034
  40. [40] Rüschendorf, L., B. Schweizer, and M. Taylor (Eds.) (1996). Distributions with FixedMarginals and Related Topics, Hayward, CA. Inst. Math. Statist. 
  41. [41] Rüschendorf, L. and W. Thomsen (1998). Closedness of sum spaces and the generalized ’Schrödinger problem’. Theory Probab. Appl. 42(3), 483–494. 
  42. [42] Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8, 229–231. Zbl0100.14202
  43. [43] Strasser, H. (1985). Mathematical Theory of Statistics: Statistical Experiments and Asymptotic Decision Theory. Walter de Gruyter & Co., Berlin. Zbl0594.62017
  44. [44] Stute, W. (1984). The oscillation behavior of empirical processes: the multivariate case. Ann. Probab. 12, 361–379. [Crossref] Zbl0533.62037

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