Convolution Bounds on Quantile Aggregation

References

• Bartl D, Kupper M, Lux T, Papapantoleon A (2022) Marginal and dependence uncertainty: Bounds, optimal transport, and sharpness. SIAM J. Control Optim. 60(1):410–434.Crossref, Google Scholar
• Basak S, Shapiro A (2001) Value-at-risk-based risk management: Optimal policies and asset prices. Rev. Financial Stud. 14(2):371–405.Crossref, Google Scholar
• Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Ben-Tal A, Den Hertog D, De Waegenaere A, Melenberg B, Rennen G (2013) Robust solutions of optimization problems affected by uncertain probabilities. Management Sci. 59(2):341–357.Link, Google Scholar
• Bernard C, Jiang X, Wang R (2014) Risk aggregation with dependence uncertainty. Insurance Math. Econom. 54:93–108.Crossref, Google Scholar
• Bernard C, Rüschendorf L, Vanduffel S (2017a) VaR bounds with variance constraint. J. Risk Insurance 84(3):923–959.Crossref, Google Scholar
• Bernard C, Rüschendorf L, Vanduffel S, Wang R (2017b) Risk bounds for factor models. Finance Stochastics 21(3):631–659.Crossref, Google Scholar
• Bertsimas D, Popescu I (2005) Optimal inequalities in probability theory: A convex optimization approach. SIAM J. Optim. 15(3):780–804.Crossref, Google Scholar
• Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev. 53(3):464–501.Crossref, Google Scholar
• Bertsimas D, Gupta V, Kallus N (2018) Robust sample average approximation. Math. Program. 171(1–2):217–282.Crossref, Google Scholar
• Blanchet J, Murthy K (2019) Quantifying distributional model risk via optimal transport. Math. Oper. Res. 44(2):565–600.Link, Google Scholar
• Blanchet J, He F, Murthy K (2020) On distributionally robust extreme value analysis. Extremes 23:317–347.Crossref, Google Scholar
• Blanchet J, Kang Y, Murthy K (2019a) Robust Wasserstein profile inference and applications to machine learning. J. Appl. Probab. 56(3):830–857.Crossref, Google Scholar
• Blanchet J, Glynn PW, Yan J, Zhou Z (2019b) Multivariate distributionally robust convex regression under absolute error loss. Proc. 33rd Internat. Conf. Neural Inform. Processing Systems (Curran Associates Inc., Red Hook, NY), 11817–11826.Google Scholar
• Boerma J, Tsyvinski A, Zimin AP (2021) Sorting with team formation. Preprint, submitted September 6, https://arxiv.org/abs/2109.02730.Google Scholar
• Boerma J, Tsyvinski A, Wang R, Zhang Z (2023) Composite sorting. Preprint, submitted March 12, https://arxiv.org/abs/2303.06701.Google Scholar
• Chen Y, Liu P, Liu Y, Wang R (2022) Ordering and inequalities of mixtures on risk aggregation. Math. Finance 32(1):421–451.Crossref, Google Scholar
• Chen W, Sim M, Sun J, Teo CP (2010) From CVaR to uncertainty set: Implications in joint chance-constrained optimization. Oper. Res. 58(2):470–485.Link, Google Scholar
• Cont R, Deguest R, Scandolo G (2010) Robustness and sensitivity analysis of risk measurement procedures. Quant. Finance 10(6):593–606.Crossref, Google Scholar
• de Castro L, Galvao AF (2019) Dynamic quantile models of rational behavior. Econometrica 87:1893–1939.Crossref, Google Scholar
• de Castro L, Galvao AF, Noussair C, Qiao L (2022) Do people maximize quantiles? Games Econom. Behav. 132:22–40.Crossref, Google Scholar
• Delage E, Mannor S (2010) Percentile optimization for Markov decision processes with parameter uncertainty. Oper. Res. 58(1):203–213.Link, Google Scholar
• Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3):595–612.Link, Google Scholar
• Doan XV, Natarajan K (2012) On the complexity of nonoverlapping multivariate marginal bounds for probabilistic combinatorial optimization problems. Oper. Res. 60(1):138–149.Link, Google Scholar
• El Ghaoui L, Oks M, Oustry F (2003) Worst-case value-at-risk and robust portfolio optimization: A conic programming approach. Oper. Res. 51(4):543–556.Link, Google Scholar
• Embrechts P, Puccetti G (2006) Bounds for functions of dependent risks. Finance Stochastics 10:341–352.Crossref, Google Scholar
• Embrechts P, Liu H, Wang R (2018) Quantile-based risk sharing. Oper. Res. 66(4):936–949.Link, Google Scholar
• Embrechts P, Puccetti G, Rüschendorf L (2013) Model uncertainty and VaR aggregation. J. Banking Finance 37(8):2750–2764.Crossref, Google Scholar
• Embrechts P, Wang B, Wang R (2015) Aggregation-robustness and model uncertainty of regulatory risk measures. Finance Stochastics 19(4):763–790.Crossref, Google Scholar
• Embrechts P, Puccetti G, Rüschendorf L, Wang R, Beleraj A (2014) An academic response to Basel 3.5. Risks 2(1):25–48.Crossref, Google Scholar
• Esfahani PM, Kuhn D (2018) Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Math. Program. 171(1–2):115–166.Crossref, Google Scholar
• Föllmer H, Schied A (2016) Stochastic Finance. An Introduction in Discrete Time, 4th ed. (Walter de Gruyter, Berlin).Crossref, Google Scholar
• Gao R, Kleywegt A (2023) Distributionally robust stochastic optimization with Wasserstein distance. Math. Oper. Res. 48(2):603–655.Link, Google Scholar
• Ghosh S, Lam H (2019) Robust analysis in stochastic simulation: Computation and performance guarantees. Oper. Res. 67(1):232–249.Link, Google Scholar
• Glasserman P, Xu X (2014) Robust risk measurement and model risk. Quant. Finance 14(1):29–58.Crossref, Google Scholar
• Goh J, Sim M (2010) Distributionally robust optimization and its tractable approximations. Oper. Res. 58(4):902–917.Link, Google Scholar
• Hu Z, Hong LJ (2013) Kullback-Leibler divergence constrained distributionally robust optimization. Optim. Online. http://www.optimization-online.org/DB_FILE/2012/11/3677.pdf.Google Scholar
• Jakobsons E, Han X, Wang R (2016) General convex order on risk aggregation. Scandinavian Actuarial J. 2016(8):713–740.Crossref, Google Scholar
• Jiang R, Guan Y (2016) Data-driven chance constrained stochastic program. Math. Program. 158(1–2):291–327.Crossref, Google Scholar
• Kremer M (1993) The O-Ring theory of economic development. Quart. J. Econom. 108(3):551–575.Crossref, Google Scholar
• Lam H (2016) Robust sensitivity analysis for stochastic systems. Math. Oper. Res. 41(4):1248–1275.Link, Google Scholar
• Lam H, Mottet C (2017) Tail analysis without parametric models: A worst-case perspective. Oper. Res. 65(6):1696–1711.Link, Google Scholar
• Li B, Jiang R, Mathieu JL (2019) Ambiguous risk constraints with moment and unimodality information. Math. Program. 173(1–2):151–192.Crossref, Google Scholar
• Liu F, Wang R (2021) A theory for measures of tail risk. Math. Oper. Res. 46(3):1109–1128.Link, Google Scholar
• Makarov GD (1981) Estimates for the distribution function of the sum of two random variables with given marginal distributions. Theory Probab. Appl. 26:803–806.Crossref, Google Scholar
• McNeil AJ, Frey R, Embrechts P (2015) Quantitative Risk Management: Concepts, Techniques and Tools, revised edition (Princeton University Press, Princeton, NJ).Google Scholar
• Mishra VK, Natarajan K, Padmanabhan D, Teo C-P, Li X (2014) On theoretical and empirical aspects of marginal distribution choice models. Management Sci. 173(1–2):151–192.Google Scholar
• Nemirovski A, Shapiro A (2007) Convex approximations of chance constrained programs. SIAM J. Optim. 17(4):969–996.Crossref, Google Scholar
• Pflug GC, Pohl M (2018) A review on ambiguity in stochastic portfolio optimization. Set-Valued Variational Anal. 26(4):733–757.Crossref, Google Scholar
• Popescu I (2005) A semidefinite programming approach to optimal-moment bounds for convex classes of distributions. Math. Oper. Res. 30(3):632–657.Link, Google Scholar
• Puccetti G, Rüschendorf L (2012) Computation of sharp bounds on the distribution of a function of dependent risks. J. Comput. Appl. Math. 236(7):1833–1840.Crossref, Google Scholar
• Puccetti G, Rüschendorf L (2013) Sharp bounds for sums of dependent risks. J. Appl. Probab. 50(1):42–53.Crossref, Google Scholar
• Puccetti G, Wang R (2015) Extremal dependence concepts. Statist. Sci. 30(4):485–517.Crossref, Google Scholar
• Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J. Banking Finance 26(7):1443–1471.Crossref, Google Scholar
• Rostek M (2010) Quantile maximization in decision theory. Rev. Econom. Stud. 77:339–371.Crossref, Google Scholar
• Rüschendorf L (1982) Random variables with maximum sums. Adv. Appl. Probab. 14(3):623–632.Crossref, Google Scholar
• Rüschendorf L (2013) Mathematical Risk Analysis, Springer Series in Operations Research and Financial Engineering (Springer-Verlag, Berlin, Heidelberg).Crossref, Google Scholar
• Shapiro A, Dentcheva D, Ruszczynski A (2021) Lectures on Stochastic Programming: Modeling and Theory (Society for Industrial and Applied Mathematics, Philadelphia).Crossref, Google Scholar
• Van Parys BPG, Goulart PJ, Kuhn D (2016) Generalized Gauss inequalities via semidefinite programming. Math. Program. 156(1–2):271–302.Crossref, Google Scholar
• Vovk V, Wang R (2020) Combining p-values via averaging. Biometrika 107(4):791–808.Crossref, Google Scholar
• Vovk V, Wang B, Wang R (2022) Admissible ways of merging p-values under arbitrary dependence. Ann. Statist. 50(1):351–375.Crossref, Google Scholar
• Wang B, Wang R (2011) The complete mixability and convex minimization problems with monotone marginal densities. J. Multivariate Anal. 102(10):1344–1360.Crossref, Google Scholar
• Wang B, Wang R (2016) Joint mixability. Math. Oper. Res. 41(3):808–826.Link, Google Scholar
• Wang R, Bignozzi V, Tsakanas A (2015) How superadditive can a risk measure be? SIAM J. Financial Math. 6:776–803.Crossref, Google Scholar
• Wang R, Zitikis R (2021) An axiomatic foundation for the expected shortfall. Management Sci. 67(3):1413–1429.Link, Google Scholar
• Wang R, Peng L, Yang J (2013) Bounds for the sum of dependent risks and worst value-at-risk with monotone marginal densities. Finance Stochastics 17(2):395–417.Crossref, Google Scholar
• Wiesemann W, Kuhn D, Sim M (2014) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.Link, Google Scholar
• Zhu S, Fukushima M (2009) Worst-case conditional value-at-risk with application to robust portfolio management. Oper. Res. 57(5):1155–1168.Link, Google Scholar
• Zymler S, Kuhn D, Rustem B (2013) Worst-case value-at-risk of nonlinear portfolios. Management Sci. 59(1):172–188.Link, Google Scholar