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Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2015-09-17
zaakceptowano
2015-10-08
online
2015-10-29
Twórcy
  • Faculty of Economics & Management, Free University of Bozen/Bolzano, Italy
  • Department of Economics, Management and Quantitative Methods, University of
    Milan
  • Chair of Mathematical Finance, Technische Universität München, Germany
Bibliografia
  • [1] Andersen, P. K., O. Borgan, R. D. Gill, and N. Keiding (2012). Statistical Models Based on Counting Processes. Springer-Verlag, New York.
  • [2] Bickel, P. J., Y. Ritov, and J. A. Wellner (1991). Efficient estimation of linear functionals of a probability measure P with knownmarginal distributions. Ann. Statist. 19(3), 1316–1346. [Crossref]
  • [3] Brenier, Y. (1991). Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl.Math. 44(4), 375–417.
  • [4] Bruss, F. T. and L. Rüschendorf (2010). On the perception of time. Gerontology 56(4), 361–370.[Crossref]
  • [5] Dall’Aglio, G., S. Kotz, and G. Salinetti (Eds.) (1991). Advances in Probability Distributions with Given Marginals. KluwerAcademic Publishers Group, Dordrecht.
  • [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.
  • [7] Deming, W. E. and F. F. Stephan (1940). On a least squares adjustment of a sampled frequency table when the expectedmarginal totals are known. Ann. Math. Stat. 11(4), 427–444.[Crossref]
  • [8] Döhler, S. and L. Rüschendorf (2003). Nonparametric estimation of regression functions in point process models. Stat.Inference Stoch. Process. 6(3), 291–307.
  • [9] Durante, F. and C. Sempi (2010). Copula theory: an introduction. In Copula Theory and Its Applications, Volume 198 ofLecture Notes in Statistics, pp. 3–31. Springer, Berlin.
  • [10] Embrechts, P. and G. Puccetti (2006). Bounds for functions of dependent risks. Finance Stoch. 10(3), 341–352.
  • [11] Embrechts, P., G. Puccetti, and L. Rüschendorf (2013). Model uncertainty and VaR aggregation. J. Bank. Financ. 37(8), 2750–2764.[WoS][Crossref]
  • [12] Fermanian, J.-D., D. Radulovic, M. Wegkamp (2004). Weak convergence of empirical copula processes. Bernoulli 10(5),847–860.[Crossref]
  • [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]
  • [14] Goll, T. and L. Rüschendorf (2001). Minimax and minimal distance martingale measures and their relationship to portfoliooptimization. Finance Stoch. 5(4), 557–581.
  • [15] Gray, L. and D. Wilson (1980). Nonnegative factorization of positive semidefinite nonnegative matrices. Linear AlgebraAppl. 31, 119 – 127.
  • [16] Grenander, U. (1968). Probabilities on Algebraic Structures (2nd edition). Almqvist & Wiksell, Stockholm and John Wiley,New York.
  • [17] Hall, P. (1935). On representatives of subsets. J. London Math. Soc. s1-10(1), 26–30.
  • [18] Hardy, G. H., J. E. Littlewood, and G. Pólya (1952). Inequalities (2nd edition). Cambridge University Press, Camdridge.
  • [19] Holtrode, R. and L. Rüschendorf (1993). Differentiablity of point process models and asymptotic efficiency of differentiablefunctionals. Statistics 24(1), 17–42.[Crossref]
  • [20] Iosifescu, M. and P. Tautu (1973). Stochastic Processes and Applications in Biology and Medicine. Springer-Verlag, Berlin-New York.
  • [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]
  • [22] Kellerer, H. G. (1984). Duality theorems for marginal problems. Z. Wahrsch. Verw. Gebiete 67(4), 399–432.[Crossref]
  • [23] Kolmogorov, A. N. (1957). On the representation of continuous functions of many variables by superposition of continuousfunctions of one variable and addition. Dokl. Akad. Nauk SSSR 114, 953–956.
  • [24] Linnik, Y. V. (1975). Problems of Analytical Statistics. Statistical Publishing Society, Calcutta.
  • [25] Mainik, G., G. Mitov, and L. Rüschendorf (2015). Portfolio optimization for heavy-tailed assets: Extreme risk indexvs. Markowitz. J. Empirical Finance 32, 115–134.
  • [26] Mainik, G. and L. Rüschendorf (2010). Onoptimal portfolio diversificationwith respect to extreme risks. Finance Stoch. 14(4),593–623.
  • [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.
  • [28] Pitt, L. D. (1982). Positively correlated normal variables are associated. Ann. Probab. 10, 496–499.[Crossref]
  • [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]
  • [30] Rachev, S. T. and L. Rüschendorf (1998). Mass Transportation Problems. Vol. I–II. Springer, New York.
  • [31] Rüschendorf, L. (1976). Asymptotic distributions of multivariate rank order statistics. Ann. Statist. 4, 912–923.[Crossref]
  • [32] Rüschendorf, L. (1981a). Sharpness of Fréchet bounds. Z. Wahrsch. Verw. Gebiete 57(2), 293–302.[Crossref]
  • [33] Rüschendorf, L. (1981b). Stochastically ordered distributions and monotonicity of the OC-function of sequential probabilityratio tests. Math. Operationsforsch. Statist. Ser. Statist. 12(3), 327–338.
  • [34] Rüschendorf, L. (1982). Random variables with maximum sums. Adv. Appl. Probab. 14, 623–632.[Crossref]
  • [35] Rüschendorf, L. (1991). Fréchet-bounds and their applications. In Advances in Probability Distributions with GivenMarginals, Volume 67, pp. 151–187. Dordrecht: Kluwer Acad. Publ.
  • [36] Rüschendorf, L. (1995). Convergence of the iterative proportional fitting procedure. Ann. Statist. 23, 1160–1174.[Crossref]
  • [37] Rüschendorf, L. (2013). Mathematical Risk Analysis. Dependence, Risk Bounds, Optimal Allocations and Portfolios. Springer,Heidelberg.
  • [38] Rüschendorf, L. (2014). Mathematische Statistik. Springer, Berlin.
  • [39] Rüschendorf, L. and S. T. Rachev (1990). A characterization of random variables with minimum L2-distance. J. MultivariateAnal. 32(1), 48–54.[Crossref]
  • [40] Rüschendorf, L., B. Schweizer, and M. Taylor (Eds.) (1996). Distributions with FixedMarginals and Related Topics, Hayward,CA. Inst. Math. Statist.
  • [41] Rüschendorf, L. and W. Thomsen (1998). Closedness of sum spaces and the generalized ’Schrödinger problem’. TheoryProbab. Appl. 42(3), 483–494.
  • [42] Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8, 229–231.
  • [43] Strasser, H. (1985). Mathematical Theory of Statistics: Statistical Experiments and Asymptotic Decision Theory. Walter deGruyter & Co., Berlin.
  • [44] Stute, W. (1984). The oscillation behavior of empirical processes: the multivariate case. Ann. Probab. 12, 361–379.[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_demo-2015-0013
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