Center-outward quantiles and the measurement of multivariate risk

Insurance: Mathematics and Economics - Tập 95 - Trang 79-100 - 2020
J. Beirlant1,2, S. Buitendag3, E. del Barrio4, M. Hallin5, F. Kamper6
1Department of Mathematics, KU Leuven, Belgium
2Department of Mathematical Statistics and Actuarial Science, University of the Free State, South Africa
3Capitec Bank, South Africa
4IMUVA, Universidad de Valladolid, Spain
5ECARES, Université libre de Bruxelles, Belgium
6Department of Statistics and Actuarial Science, University of Stellenbosch, South Africa

Tài liệu tham khảo

Beirlant, 2004 Bertsekas, 1992, Auction algoritms for network flow problems: a tutorial introduction, Comput. Optim. Appl., 1, 7, 10.1007/BF00247653 Boyd, 2004 Charpentier, 2018 Chernozhukov, 2017, Monge–Kantorovich depth, quantiles, ranks, and signs, Ann. Statist., 45, 223, 10.1214/16-AOS1450 Cuesta-Albertos, 1993, Optimal coupling of multivariate distributions and stochastic processes, J. Multivariate Anal., 46, 335, 10.1006/jmva.1993.1064 de Haan, 2006 del Barrio, E., Albertos, J.Cuesta., Hallin, M., Matrán, C., 2018. Smooth cyclically monotone interpolation and empirical center-outward distribution functions. Working Papers ECARES 2018-15, ULB, https://ideas.repec.org/p/eca/wpaper/2013-271399.html. del Barrio, 2019, Central limit theorems for empirical transportation cost in general dimension, Ann. Probab., 47, 926, 10.1214/18-AOP1275 Dudley, 2004 Einmahl, 1992, Generalized quantile processes, Ann. Statist., 20, 1062, 10.1214/aos/1176348670 Ekeland, 2012, Comonotonic measures of multivariate risks, Math. Finance, 22, 109, 10.1111/j.1467-9965.2010.00453.x Embrechts, 1997 Figalli, 2018, On the continuity of center-outward distribution and quantile functions, Nonlinear Anal. TMA, 177, 413, 10.1016/j.na.2018.05.008 Gushchin, 2017, Integrated quantile functions: properties and applications, 285 Hallin, M., 2017. Distribution and quantile functions, ranks and signs in Rd: A measure transportation approach. Working Papers ECARES 2017-34, ULB, https://ideas.repec.org/p/eca/wpaper/2013-258262.html. Hallin, 2020 Kusuoka, 2001, On law invariant coherent risk measures, Adv. Math. Econ., 3, 83, 10.1007/978-4-431-67891-5_4 Mazumder, 2019, A computational framework for multivariate convex regression and its variants, J. Amer. Stat. Assoc., 114, 318, 10.1080/01621459.2017.1407771 McCann, 1995, Existence and uniqueness of monotone measure-preserving maps, Duke Math. J., 80, 309, 10.1215/S0012-7094-95-08013-2 Rockafellar, 1966, Characterization of the subdifferential of convex functions, Pacific J. Math., 17, 497, 10.2140/pjm.1966.17.497 Rockafellar, 1970 Rüschendorf, 2006, Law invariant convex risk measures for portfolio vectors, Statist. Decisions, 24, 97, 10.1524/stnd.2006.24.1.97 Villani, 2009