×

zbMATH — the first resource for mathematics

Buffered probability of exceedance: mathematical properties and optimization. (English) Zbl 1395.90191

MSC:
90C15 Stochastic programming
90C25 Convex programming
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] J. R. Davis and S. Uryasev, Analysis of tropical storm damage using buffered probability of exceedance, Nat. Hazards, 2015, pp. 1–19.
[2] E. Delage, D. Kuhn, and W. Wiesemann, “Dice”-sion Making under Uncertainty: When Can a Random Decision Reduce Risk?, 2016, .
[3] D. Dentcheva and G. Martinez, Two-stage stochastic optimization problems with stochastic ordering constraints on the recourse, European J. Oper. Res., 219 (2012), pp. 1–8. · Zbl 1244.90174
[4] D. Dentcheva and A. Ruszczynski, Optimization with stochastic dominance constraints, SIAM J. Optim., 14 (2003), pp. 548–566. · Zbl 1055.90055
[5] D. Dentcheva and A. Ruszczynski, Convexification of stochastic ordering, C. R. Acad. Bulgare Sci., 57 (2004), pp. 4–11. · Zbl 1083.90031
[6] H. Föllmer and A. Schied, Convex measures of risk and trading constraints, Finance Stoch., 6 (2002), pp. 429–447. · Zbl 1041.91039
[7] H. Föllmer and A. Schied, Stochastic Finance: An Introduction in Discrete Time, Walter de Gruyter, Berlin, 2011.
[8] N. Langenberg and R. Tichatschke, Interior proximal methods for quasiconvex optimization, J. Global Optim., 52 (2012), pp. 641–661. · Zbl 1279.90135
[9] K. Miettinen, Nonlinear Multiobjective Optimization, Vol. 12, Springer, New York, 2012. · Zbl 1282.90166
[10] A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs, SIAM J. Optim., 17 (2006), pp. 969–996. · Zbl 1126.90056
[11] M. Norton, A. Mafusalov, and S. Uryasev, Cardinality of Upper Average and Application to Network Optimization, Research report 2015-1, ISE Department, University of Florida, 2015. · Zbl 1391.90407
[12] M. Norton, A. Mafusalov, and S. Uryasev, Soft margin support vector classification as buffered probability minimization, J. Mach. Learn. Res., 18 (2017), pp. 1–43. · Zbl 1434.68440
[13] M. Norton and S. Uryasev, Maximization of AUC and Buffered AUC in Classification, Research report 2014-2, ISE Department, University of Florida, 2014.
[14] W. Ogryczak and A. Ruszczynski, Dual stochastic dominance and related mean-risk models, SIAM J. Optim., 13 (2002), pp. 60–78. · Zbl 1022.91017
[15] I. Olkin and A. W. Marshall, Inequalities: Theory of Majorization and its Applications, Vol. 143, Academic Press, New York, 2016. · Zbl 0437.26007
[16] K. Pavlikov and S. Uryasev, CVaR Distance Between Univariate Probability Distributions and Approximation Problems, Research report 2015-6, ISE Department, University of Florida, 2015. · Zbl 1391.62025
[17] R. T. Rockafellar, Conjugate Duality and Optimization, SIAM, Philadelphia, 1974. · Zbl 0296.90036
[18] R. T. Rockafellar, Convex Analysis, Princeton Landmarks Math., Princeton University Press, Princeton, NJ, 1997. · Zbl 0932.90001
[19] R. T. Rockafellar, Safeguarding strategies in risky optimization, in Proceedings of the International Workshop on Engineering Risk Control and Optimization, Gainesville, FL, 2009.
[20] R. T. Rockafellar and J. O. Royset, On buffered failure probability in design and optimization of structures, Reliab. Eng. Syst. Safe., 95 (2010), pp. 499–510.
[21] R. T. Rockafellar and J. O. Royset, Random variables, monotone relations, and convex analysis, Math. Program., 148 (2014), pp. 297–331. · Zbl 1330.60009
[22] R. T. Rockafellar and S. Uryasev, Conditional value-at-risk for general loss distributions, J. Bank. Finance, 26 (2002), pp. 1443–1471.
[23] R. T. Rockafellar and S. Uryasev, The fundamental risk quadrangle in risk management, optimization and statistical estimation, Surv. Oper. Res. Manag. Sci., 18 (2013).
[24] J. V. Ryff, Orbits of l \(1\)-functions under doubly stochastic transformation, Trans. Amer. Math. Soc., 117 (1965), pp. 92–100. · Zbl 0135.18804
[25] M. Shaked and J. G. Shanthikumar, Stochastic Orders, Springer, New York, 2007.
[26] D. Shang, V. Kuzmenko, and S. Uryasev, Cash flow matching with risks controlled by buffered probability of exceedance and conditional value-at-risk, Ann. Oper. Res., 260 (2018), pp. 501–514. · Zbl 1404.91269
[27] S. Uryasev, Buffered Probability of Exceedance and Buffered Service Level: Definitions and Properties, Research report 2014-3, ISE Department, University of Florida, 2014.
[28] M. Zabarankin and S. Uryasev, Statistical Decision Problems, Springer, New York, 2014.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.