Extreme-Case Distortion Risk Measures: A Unification and Generalization of Closed-Form Solutions
Published Online:23 Nov 2023https://doi.org/10.1287/moor.2022.0156
References
- [1] (2002) Spectral measures of risk: A coherent representation of subjective risk aversion. J. Banking Finance 26(7):1505–1518.Crossref, Google Scholar
- [2] (1999) Coherent measures of risk. Math. Finance 9(3):203–228.Crossref, Google Scholar
- [3] (2014) Beyond value-at-risk: Gluevar distortion risk measures. Risk Anal. 34(1):121–134.Crossref, Google Scholar
- [4] (2016) What attitudes to risk underlie distortion risk measure choices? Insurance Math. Econom. 68:101–109.Crossref, Google Scholar
- [5] (2010) Models for minimax stochastic linear optimization problems with risk aversion. Math. Oper. Res. 35(3):580–602.Link, Google Scholar
- [6] (2011) Tight bounds for some risk measures, with applications to robust portfolio selection. Oper. Res. 59(4):847–865.Link, Google Scholar
- [7] (2010) Robustness and sensitivity analysis of risk measurement procedures. Quant. Finance 10(6):593–606.Crossref, Google Scholar
- [8] (2021) On the heavy-tail behavior of the distributionally robust newsvendor. Oper. Res. 69(4):1077–1099.Link, Google Scholar
- [9] (2003) Worst-case value-at-risk and robust portfolio optimization: A conic programming approach. Oper. Res. 51(4):543–556.Link, Google Scholar
- [10] (2002) Analytical bounds for two value-at-risk functionals. ASTIN Bull. 32(2):235–265.Crossref, Google Scholar
- [11] (1986) Best bounds for positive distributions with fixed moments. Insurance Math. Econom. 5(1):87–92.Crossref, Google Scholar
- [12] (2018) Closed-form solutions for worst-case law invariant risk measures with application to robust portfolio optimization. Oper. Res. 66(6):1533–1541.Link, Google Scholar
- [13] (2018) Worst-case range value-at-risk with partial information. SIAM J. Financial Math. 9(1):190–218.Crossref, Google Scholar
- [14] (2015) Quantitative Risk Management: Concepts, Techniques and Tools, revised ed. (Princeton University Press, Princeton, NJ).Google Scholar
- [15] (2008) Incorporating asymmetric distributional information in robust value-at-risk optimization. Management Sci. 54(3):573–585.Link, Google Scholar
- [16] (2010) Tractable robust expected utility and risk models for portfolio optimization. Math. Finance 20(4):695–731.Crossref, Google Scholar
- [17] (2013) Evaluations of risk measures for different probability measures. SIAM J. Optim. 23(1):530–551.Crossref, Google Scholar
- [18] (2014) Insurance pricing under ambiguity. Eur. Actuarial J. 4:335–364.Crossref, Google Scholar
- [19] (2022) Quantitative stability analysis for minimax distributionally robust risk optimization. Math. Programming 191(1):47–77.Crossref, Google Scholar
- [20] (2005) A semidefinite programming approach to optimal-moment bounds for convex classes of distributions. Math. Oper. Res. 30(3):632–657.Link, Google Scholar
- [21] (2007) Robust mean-covariance solutions for stochastic optimization. Oper. Res. 55(1):98–112.Link, Google Scholar
- [22] (2016) Worst-case conditional value-at-risk minimization for hazardous materials transportation. Transportation Sci. 50(4):1174–1187.Link, Google Scholar
- [23] (1995) Insurance pricing and increased limits ratemaking by proportional hazards transforms. Insurance Math. Econom. 17(1):43–54.Crossref, Google Scholar
- [24] (2000) A class of distortion operators for pricing financial and insurance risks. J. Risk Insurance 67(1):15–36.Crossref, Google Scholar
- [25] (2023) Preference robust distortion risk measure and its application. Math. Finance 33(2):389–434.Crossref, Google Scholar
- [26] (2014) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.Link, Google Scholar
- [27] (1987) The dual theory of choice under risk. Econometrica 55(1):95–115.Crossref, Google Scholar
- [28] (2009) Worst-case conditional value-at-risk with application to robust portfolio management. Oper. Res. 57(5):1155–1168.Link, Google Scholar
- [29] (2013) Worst-case value at risk for nonlinear portfolios. Management Sci. 59(1):172–188.Link, Google Scholar

