References
- Artzner, P., Delbaen, F., Eber, J.M. and Heath, D., Coherent measures of risk. Math. Finan., 1999, 9, 203–228. doi: https://doi.org/10.1111/1467-9965.00068
- Belomestny, D. and Krätschmer, V., Central limit theorems for law-invariant coherent risk measures. J. Appl. Probab., 2012, 49, 1–21. doi: https://doi.org/10.1239/jap/1331216831
- Ben-Tal, A. and Teboulle, M., An old-new concept of convex risk measures: The optimized certainty equivalent. Math. Finan., 2007, 17, 449–476. doi: https://doi.org/10.1111/j.1467-9965.2007.00311.x
- Beutner, E. and Zähle, H., A modified functional delta method and its application to the estimation of risk functionals. J. Multivar. Anal., 2010, 101, 2452–2463. doi: https://doi.org/10.1016/j.jmva.2010.06.015
- Boente, G., Fraiman, R. and Yohai, V.J. et al., Qualitative robustness for stochastic processes. Ann. Stat., 1987, 15, 1293–1312. doi: https://doi.org/10.1214/aos/1176350506
- Chen, C., Iyengar, G. and Moallemi, C.C., An axiomatic approach to systemic risk. Manage. Sci., 2013, 59, 1373–1388. doi: https://doi.org/10.1287/mnsc.1120.1631
- Claus, M., Advancing stability analysis of mean-risk stochastic programs: Bilevel and two-stage models. PhD Thesis, University of Duisburg-Essen, 2016.
- Claus, M., Krätschmer, V. and Schultz, R., Weak continuity of risk functionals with applications to stochastic programming. SIAM. J. Optim., 2017, 27, 91–109. doi: https://doi.org/10.1137/15M1048689
- Cont, R., Deguest, R. and Scandolo, G., Robustness and sensitivity analysis of risk measurement procedures. Quant. Finance, 2010, 10, 593–606. doi: https://doi.org/10.1080/14697681003685597
- Delage, E., Kuhn, D. and Wiesemann, W., “Dice”-sion–making under uncertainty: When can a random decision reduce risk?. Manage. Sci., 2019, 65, 3282–3301. doi: https://doi.org/10.1287/mnsc.2018.3108
- Filipović, D. and Svindland, G., The canonical model space for law-invariant convex risk measures is L1. Math. Finan., 2012, 22, 585–589. doi: https://doi.org/10.1111/j.1467-9965.2012.00534.x
- Föllmer, H. and Schied, A., Convex measures of risk and trading constraints. Finan. Stoch., 2002, 6, 429–447. doi: https://doi.org/10.1007/s007800200072
- Föllmer, H. and Weber, S., The axiomatic approach to risk measures for capital determination. Annu. Rev. Finan. Econ., 2015, 7, 301–337. doi: https://doi.org/10.1146/annurev-financial-111914-042031
- Gibbs, A.L. and Su, F.E., On choosing and bounding probability metrics. Int. Stat. Rev., 2002, 70, 419–435. doi: https://doi.org/10.1111/j.1751-5823.2002.tb00178.x
- Guo, S. and Xu, H., Statistical robustness in utility preference robust optimization models. Math. Program., 2020. https://doi.org/10.1007/s10107-020-01555-5
- Guo, S., Xu, H. and Zhang, L., Convergence analysis for mathematical programs with distributionally robust chance constraint. SIAM. J. Optim., 2017, 27, 784–816. doi: https://doi.org/10.1137/15M1036592
- Hampel, F.R., A general qualitative definition of robustness. Ann. Math. Stat., 1971, 42(6), 1887–1896. doi: https://doi.org/10.1214/aoms/1177693054
- Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. and Stahel, W.A., Robust statistics: The approach based on influence functions, Vol. 196, 2011 (John Wiley & Sons).
- Huber, P.J. and Ronchetti, E.M., Robust Statistics, 2011 (Springer).
- Inoue, A., On the worst conditional expectation. J. Math. Anal. Appl., 2003, 286, 237–247. doi: https://doi.org/10.1016/S0022-247X(03)00477-3
- Krätschmer, V., Schied, A. and Zähle, H., Qualitative and infinitesimal robustness of tail-dependent statistical functionals. J. Multivar. Anal., 2012, 103, 35–47. doi: https://doi.org/10.1016/j.jmva.2011.06.005
- Krätschmer, V., Schied, A. and Zähle, H., Comparative and qualitative robustness for law-invariant risk measures. Finan. Stochast., 2014, 18, 271–295. doi: https://doi.org/10.1007/s00780-013-0225-4
- Krätschmer, V., Schied, A. and Zähle, H., Domains of weak continuity of statistical functionals with a view toward robust statistics. J. Multivar. Anal., 2017, 158, 1–19. doi: https://doi.org/10.1016/j.jmva.2017.02.005
- Maronna, R.A., Martin, R.D., Yohai, V.J. and Salibián-Barrera, M., Robust statistics: Theory and methods (with R), 2019 (John Wiley & Sons).
- Mattila, P., Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability, Vol. 44, 1999 (Cambridge University Press).
- Mizera, I., Qualitative robustness and weak continuity: The extreme unction. Nonparametr. Robust. Modern Stat. Inf. Time Series Anal.: A Festschrift in Honor of Professor Jana Jurecková, 2010, 7, 169–181.
- Panaretos, V.M. and Zemel, Y., Statistical aspects of Wasserstein distances. Annu. Rev. Stat. Appl., 2019, 6, 405–431. doi: https://doi.org/10.1146/annurev-statistics-030718-104938
- Pflug, G.C. and Pichler, A., Approximations for probability distributions and stochastic optimization problems. In Stochastic Optimization Methods in Finance and Energy, pp. 343–387, 2011 (Springer: New York, NY).
- Rachev, S.T., Probability Metrics and the Stability of Stochastic Models, Vol. 269, 1991 (John Wiley & Son Ltd).
- Römisch, W., Stability of stochastic programming problems. Handb. Oper. Res. Manage. Sci., 2003, 10, 483–554.
- Ruszczyński, A. and Shapiro, A., Optimization of convex risk functions. Math. Operat. Res., 2006, 31, 433–452. doi: https://doi.org/10.1287/moor.1050.0186
- Strohriegl, K. and Hable, R., Qualitative robustness of estimators on stochastic processes. Metrika, 2016, 79, 895–917. doi: https://doi.org/10.1007/s00184-016-0582-z
- Wang, W. and Xu, H., Robust spectral risk optimization when information on risk spectrum is incomplete. SIAM. J. Optim., 2020, 30, 3198–3229. doi: https://doi.org/10.1137/19M1284270
- Zähle, H., Rates of almost sure convergence of plug-in estimates for distortion risk measures. Metrika, 2011, 74, 267–285. doi: https://doi.org/10.1007/s00184-010-0302-z
- Zähle, H., Qualitative robustness of von Mises statistics based on strongly mixing data. Stat. Pap., 2014, 55, 157–167. doi: https://doi.org/10.1007/s00362-012-0478-6
- Zähle, H., Qualitative robustness of statistical functionals under strong mixing. Bernoulli, 2015, 21, 1412–1434. doi: https://doi.org/10.3150/14-BEJ608
- Zähle, H., A definition of qualitative robustness for general point estimators, and examples. J. Multivar. Anal., 2016, 143, 12–31. doi: https://doi.org/10.1016/j.jmva.2015.08.004