Robustness in the Optimization of Risk Measures
Published Online:15 Nov 2021https://doi.org/10.1287/opre.2021.2147
References
- (2010) Manufacturing Tail Risk: A Perspective on the Financial Crisis of 2007-2009 (Now Publishers Inc., Hanover, MA).Google Scholar
- (2018) Rogue traders vs. value-at-risk and expected shortfall. Risk Magazine (April 2018), https://www.risk.net/risk-management/5478266/rogue-traders-versus-value-at-risk-and-expected-shortfall.Google Scholar
- (1963) Uncertainty and the welfare economics of medical care. Amer. Econom. Rev. 53(5):941–973.Google Scholar
- (1954) Existence of an equilibrium for a competitive economy. Econometrica 22(3):265–290.Crossref, Google Scholar
- (1999) Coherent measures of risk. Math. Finance 9(3):203–228.Crossref, Google Scholar
- BCBS (2016) Standards: Minimum capital requirements for market risk. Report, Basel Committee on Banking Supervision, Bank for International Settlements, Basel.Google Scholar
- (1987) Penalty functions and duality in stochastic programming via ϕ-divergence functionals. Math. Oper. Res. 12:224–240.Link, Google Scholar
- (2007) An old-new concept of convex risk measures: The optimized certainty equivalent. Math. Finance 17(3):449–476.Crossref, Google Scholar
- (2009) Robust Optimization (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
- (2015) Optimal insurance design under rank-dependent expected utility. Math. Finance 25:154–186.Crossref, Google Scholar
- (2019) Quantifying distributional model risk via optimal transport. Math. Oper. Res. 44(2):565–600.Link, Google Scholar
- (2000) Perturbation Analysis of Optimization Problems, Springer Series in Operations Research (Springer-Verlag, New York).Crossref, Google Scholar
- (2020) Bayesian optimization of risk measures. Preprint, submitted July 10, https://arxiv.org/abs/2007.05554.Google Scholar
- (2010) Robustness and sensitivity analysis of risk measurement procedures. Quant. Finance 10(6):593–606.Crossref, Google Scholar
- (2002) The emperor has no clothes: Limits to risk modelling. J. Banking Finance 26(7):1273–1296.Crossref, Google Scholar
- (2001) An academic response to Basel II. LSE Special Paper Series May 2001, London School of Economics, London.Google Scholar
- (1976) Convex Analysis and Variational Problems (Translated from the French), Studies in Mathematics and its Applications, vol. 1 (North-Holland Publishing Co., Amsterdam).Google Scholar
- (2018) Quantile-based risk sharing. Oper. Res. 66(4):936–949.Link, Google Scholar
- (2015) Aggregation-robustness and model uncertainty of regulatory risk measures. Finance Stochastics 19(4):763–790.Crossref, Google Scholar
- (2014) An academic response to Basel 3.5. Risks 2(1):25–48.Crossref, Google Scholar
- (2015) What is the best risk measure in practice? A comparison of standard measures. J. Risk 18(2):31–60.Crossref, Google Scholar
- (2016) Higher order elicitability and Osband’s principle. Ann. Statist. 44(4):1680–1707.Crossref, Google Scholar
- (2002) Convex measures of risk and trading constraints. Finance Stoch. 6(4):429–447.Crossref, Google Scholar
- (2016) Stochastic Finance. An Introduction in Discrete Time, 4th ed. (de Gruyter, Berlin).Crossref, Google Scholar
- (2010) Distributionally robust optimization and its tractable approximations. Oper. Res. 58(4):902–917.Link, Google Scholar
- (1984) Problems of monetary management: the UK experience. Monetary Theory and Practice (Palgrave, London), 91–121.Crossref, Google Scholar
- (2013) Kullback-Leibler divergence constrained distributionally robust optimization. Accessed September 6, 2021, DOI: http://www.optimization-online.org/DB_FILE/2012/11/3677.pdf.Google Scholar
- IAIS (2014) Risk-based global insurance capital standard (Consultation Document December 2014, International Association of Insurance Supervisors, Basel).Google Scholar
- (2016) On the measurement of economic tail risk. Oper. Res. 64(5):1056–1072.Link, Google Scholar
- (2013) External risk measures and Basel accords. Math. Oper. Res. 38(3):393–417.Link, Google Scholar
- (2014) Comparative and quantitiative robustness for law-invariant risk measures. Finance Stochastics 18(2):271–295.Crossref, Google Scholar
- (2017) Domains of weak continuity of statistical functionals with a view toward robust statistics. J. Multivariate Anal. 158:1–19.Crossref, Google Scholar
- (2019) PELVE: Probability equivalent level of VaR and ES. Preprint, submitted December 12, DOI: https://dx.doi.org/10.2139/ssrn.3489566.Google Scholar
- (2015) Quantitative Risk Management: Concepts, Techniques and Tools, revised ed. (Princeton University Press, Princeton, NJ).Google Scholar
- (2008) Incorporating asymmetric distributional information in robust value-at-risk optimization. Management Sci. 54(3):573–585.Link, Google Scholar
- (2006) Infinite mean models and the LDA for operational risk. . Operational Risk 1(1):3–25.Crossref, Google Scholar
- (1987) Asymmetric least squares estimation and testing. Econometrica 55(4):819–847.Crossref, Google Scholar
- (2007) Modeling, Measuring and Managing Risk (World Scientific Publishing, Hackensack, NJ).Crossref, Google Scholar
- (2008) Robust optimization of conditional value at risk and portfolio selection. J. Banking Finance 32(10):2046–2056.Crossref, Google Scholar
- (2004) Dynamic minimization of worst conditional expectation of shortfall. Math. Finance 14(4):605–618.Crossref, Google Scholar
- (2000) Probability for Statisticians, Springer Texts in Statistics (Springer-Verlag, New York).Google Scholar
- (2009) On modeling and interpreting the economics of catastrophic climate change. Rev. Econom. Statist. 91(1):1–19.Crossref, Google Scholar
- (2014) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.Link, Google Scholar
- (2009) Worst-case conditional value-at-risk with application to robust portfolio management. Oper. Res. 57(5):1155–1168.Link, Google Scholar
- (2013) Distributionally robust joint chance constraints with second-order moment information. Math. Program. Ser. A 137:167–198.Crossref, Google Scholar

