[1]
|
A. Ahmadi-Javid, Entropic value-at-risk: A new coherent risk measure, J. Optim. Theory Appl., 155 (2012), 1105-1123.
doi: 10.1007/s10957-011-9968-2.
|
[2]
|
J. Ang, F. Meng and J. Sun, Two-stage stochastic linear programs with incomplete information on uncertainty, European J. Oper. Res., 233 (2014), 16-22.
doi: 10.1016/j.ejor.2013.07.039.
|
[3]
|
M. Ang, J. Sun and Q. Yao, On the dual representation of coherent risk measures, Ann. Oper. Res., 262 (2018), 29-46.
doi: 10.1007/s10479-017-2441-3.
|
[4]
|
D. P. Bertsekas, Convex optimization algorithms, Athena Scientific, Belmont, MA, 2015.
|
[5]
|
D. P. Bertsekas, A. Nedi and A. E. Ozdaglar, Convex analysis and optimization, Athena Scientific, Belmont, MA, 2003.
|
[6]
|
D. Bertsimas, X. V. Doan and K. Natarajan, Models for minimax stochastic linear optimization problems with risk aversion, Math. Oper. Res., 35 (2010), 580-602.
doi: 10.1287/moor.1100.0445.
|
[7]
|
D. Bertsimas and R. Freund, Data, Models, and Decisions: The Fundamentals of Management Science, South-Western College Publishing, Cincinnati, OH, 2000.
|
[8]
|
D. Bertsimas, M. Sim and M. Zhang, Adaptive distributionally robust optimization, Manag. Sci., (2018).
doi: 10.1287/mnsc.2017.2952.
|
[9]
|
G. C. Calalore, Ambiguous risk measures and optimal robust portfolios, SIAM J. Optim., 18 (2007), 853-877.
doi: 10.1137/060654803.
|
[10]
|
E. Delage and Y. Y. Ye, Distributionally robust optimization under moment uncertainty with application to data-driven problems, Oper. Res., 58 (2010), 595-612.
doi: 10.1287/opre.1090.0741.
|
[11]
|
H. Föllmer and A. Schied, Stochastic finance, Walter de Gruyter & Co., Berlin, 2002.
doi: 10.1515/9783110198065.
|
[12]
|
S. Gao, L. Kong and J. Sun, Robust two-stage stochastic linear programs with moment constraints, Optimization, 63 (2014), 829-837.
doi: 10.1080/02331934.2014.906598.
|
[13]
|
M. Grötschel, L. Lovász and and A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica, 1 (1981), 169-197.
doi: 10.1007/BF02579273.
|
[14]
|
Z. Hu and J. Hong, Kullback-Leibler divergence constrained distributionally robust optimization, Available from: http://www.optimization-online.org/DB_HTML/2012/11/3677.html.
|
[15]
|
D. Klabjan, D. Simchi-Levi and M. Song, Robust stochastic lot-sizing by means of histograms, Prod. Oper. Manag., 22 (2013), 691-710.
doi: 10.1111/j.1937-5956.2012.01420.x.
|
[16]
|
B. Li, X. Qian, J. Sun, K. L. Teo and C. Yu, A model of distributionally robust two-stage stochastic convex programming with linear recourse, Appl. Math. Model., 58 (2018), 86-97.
doi: 10.1016/j.apm.2017.11.039.
|
[17]
|
B. Li, Y. Rong, J. Sun and K. L. Teo, A distributionally robust linear receiver design for multi-access space-time block coded MIMO systems, IEEE Trans. Signal Process., 16 (2017), 464-474.
doi: 10.1109/TWC.2016.2625246.
|
[18]
|
B. Li, Y. Rong, J. Sun and K. L. Teo, A distributionally robust minimum variance beamformer design, IEEE Signal Process. Lett., 25 (2018), 105-109.
doi: 10.1109/LSP.2017.2773601.
|
[19]
|
B. Li, J. Sun, H. L. Xu and M. Zhang, A class of two-stage distributionally robust games, J. Ind. Manag. Optim., 15 (2019), 387-400.
doi: 10.3934/jimo.2018048.
|
[20]
|
A. Ling, J. Sun and X. Yang, Robust tracking error portfolio selection with worst-case downside risk measures, J. Econom. Dynam. Control, 39 (2014), 178-207.
doi: 10.1016/j.jedc.2013.11.011.
|
[21]
|
A. Ling, J. Sun, N. H. Xiu and X. Yang, Robust two-stage stochastic linear optimization with risk aversion, European J. Oper. Res., 256 (2017), 215-229.
doi: 10.1016/j.ejor.2016.06.017.
|
[22]
|
H-J. Lüthi and J. Doege, Convex risk measures for portfolio optimization and concepts of flexibility, Math. Program., 104 (2005), 541-559.
doi: 10.1007/s10107-005-0628-x.
|
[23]
|
S. Mehrotra and H. Zhang, Models and algorithms for distributionally robust least squares problems, Math. Program., 146 (2014), 123-141.
doi: 10.1007/s10107-013-0681-9.
|
[24]
|
R. T. Rockafellar, Coherent approaches to risk in optimization under uncertainty, Tutorials in Operations Research, INFORMS, 2007, 38–61.
doi: 10.1287/educ.1073.0032.
|
[25]
|
R. T. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk, J. Risk., 2 (2000), 21-42.
doi: 10.21314/JOR.2000.038.
|
[26]
|
R. T. Rockafellar and S. Uryasev, Conditional value-at-risk for general loss distributions, J. Banking & Finance, 26 (2002), 1443-1471.
doi: 10.1016/S0378-4266(02)00271-6.
|
[27]
|
W. W. Rogosinski, Moments of non-negative mass, Proc. Roy. Soc. London Ser. A, 245 (1958), 1-27.
doi: 10.1098/rspa.1958.0062.
|
[28]
|
A. Shapiro and S. Ahmed, On a class of minimax stochastic programs, SIAM J. Optim., 14 (2004), 1237-1249.
doi: 10.1137/S1052623403434012.
|
[29]
|
A. Shapiro, D. Dentcheva and A. Ruszczyski, Lectures on Stochastic Programming: Modeling and Theory, MPS/SIAM Series on Optimization, SIAM, Philadelphia, PA, 2009.
doi: 10.1137/1.9780898718751.
|
[30]
|
M. Sion, On general minimax theorems, Pacific J. Math., 8 (1958), 171-176.
doi: 10.2140/pjm.1958.8.171.
|
[31]
|
J. Sun, L. Liao and B. Rodrigues, Quadratic two-stage stochastic optimization with coherent measures of risk, Math. Program., 168 (2018), 599-613.
doi: 10.1007/s10107-017-1131-x.
|
[32]
|
W. Wiesemann, D. Kuhn and M. Sim, Distributionally robust convex optimization, Oper. Res., 62 (2014), 1358-1376.
doi: 10.1287/opre.2014.1314.
|