[1]
|
G. J. Alexander and A. M. Baptista, A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model, Manag. Sci., 50 (2004), 1261-1273.
|
[2]
|
E. Anderson, H. Xu and D. Zhang, Confidence levels for CVaR risk measures and minimax limits, manuscript, The University of Sydney, 2014. Available from: http://hdl.handle.net/2123/9943.
|
[3]
|
K. B. Athreya and S. N. Lahiri, Measure Theory and Probability Theory, Springer Texts in Statistics, Springer, New York, 2006.
|
[4]
|
J. F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems, Springer Series in Operations Research, Springer-Verlag, 2000.
doi: 10.1007/978-1-4612-1394-9.
|
[5]
|
F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
|
[6]
|
N. A. Canakgoz and J. E. Beasley, Mixed-integer programming approaches for index tracking and en-hanced indexation, European J. Oper. Res., 196 (2009), 384-399.
doi: 10.1016/j.ejor.2008.03.015.
|
[7]
|
D. Dentcheva and A. Ruszczyński, Optimization with stochastic dominance constraints, SIAM J. Optim., 14 (2003), 548-566.
doi: 10.1137/S1052623402420528.
|
[8]
|
D. Dentcheva and A. Ruszczyński, Semi-infinite probabilistic constraints: Optimality and convexification, Optimization, 53 (2004), 583-601.
doi: 10.1080/02331930412331327148.
|
[9]
|
D. Dentcheva and A. Ruszczyński, Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints, Math. Program., 99 (2004), 329-350.
doi: 10.1007/s10107-003-0453-z.
|
[10]
|
D. Dentcheva and A. Ruszczyński, Portfolio optimization with stochastic dominance constraints, J. Bank. Financ., 30 (2006), 433-451.
doi: 10.1137/S1052623402420528.
|
[11]
|
D. Dentcheva and A. Ruszczyński, Inverse cutting plane methods for optimization problems with second-order stochastic dominance constraints, Optimization, 59 (2010), 323-338.
doi: 10.1080/02331931003696350.
|
[12]
|
D. Dentcheva and A. Ruszczyński, Risk-averse portfolio optimization via stochastic dominance constraints, in Handbook of Quantitative Finance and Risk Management (eds. C. Lee, A. Lee and J. Lee), Springer, New York, (2015), 2281-2302.
|
[13]
|
C. Fábián, G. Mitra and D. Roman, Processing second-order stochastic dominance models using cutting-plane representations, Math. Program., 130 (2011), 33-57.
doi: 10.1007/s10107-009-0326-1.
|
[14]
|
M. Gugat, A parametric review on the Mangasarian-Fromovitz constraint qualification, Math. Program., 85 (1999), 643-653.
doi: 10.1007/s101070050075.
|
[15]
|
T. Homem-de-Mello and S. Mehrota, A cutting surface method for uncertain linear programs with polyhedral stochastic dominance constraints, SIAM J. Optim., 20 (2009), 1250-1273.
doi: 10.1137/08074009X.
|
[16]
|
J. Hu, T. Homen-De-Mello and S. Mehrotra, Sample average approximation of stochastic dominance constrained programs, Math. Program., 133 (2012), 171-201.
doi: 10.1007/s10107-010-0428-9.
|
[17]
|
P. Jorion, Value at Risk: The New Benchmark for Controlling Market Risk, McGraw-Hill Inc., US, 2006.
|
[18]
|
J. E. Kelley, The cutting-plane method for solving convex programs, SIAM J. Appl. Math., 8 (1960), 703-712.
doi: 10.1137/0108053.
|
[19]
|
P. Kolm, R. Tütüncü and F. Fabozzi, 60 Years of portfolio optimization: Practical challenges and current trends, European J. Oper. Res., 234 (2014), 356-371.
doi: 10.1016/j.ejor.2013.10.060.
|
[20]
|
H. Konno and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Manag. Sci., 37 (1991), 519-531.
doi: 10.1287/mnsc.37.5.519.
|
[21]
|
H. Konno, H. Shirakawa and H. Yamazaki, A mean-absolute deviation-skewness portfolio optimization model, Ann. Oper. Res., 45 (1993), 205-220.
doi: 10.1007/BF02282050.
|
[22]
|
Y. Liu and H. Xu, Stability and sensitivity analysis of stochastic programs with second order dominance constraints, Math. Program., 142 (2013), 435-460.
doi: 10.1007/s10107-012-0585-0.
|
[23]
|
H. Markowitz, Portfolio Selection, J. Finance, (1952), 77-91.
|
[24]
|
H. Markowitz, Portfolio Selection, John Wiley & Sons, New York, 1959.
|
[25]
|
K. Mosler and M. Scarsini, (eds.), Stochastic Orders and Decision under Risk, Institute of Mathematical Statistics, Hayward, CA, 1991.
|
[26]
|
W. Ogryczak and A Ruszczyński, From stochastic dominance to mean-risk models: Semideviations as risk measures, Euro. J. Oper. Res., 116 (1999), 33-50.
doi: 10.1016/S0377-2217(98)00167-2.
|
[27]
|
W. Ogryczak and A Ruszczyński, Dual stochastic dominance and related mean-risk models, SIAM J. Optim., 13 (2002), 60-78.
doi: 10.1137/S1052623400375075.
|
[28]
|
R. T. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk, J. Risk, 2 (2000), 21-41.
doi: 10.21314/JOR.2000.038.
|
[29]
|
D. Roman, K. Darby-Dowman and G. Mitra, Portfolio construction based on stochastic dominance and target return distributions, Math. Program., 108 (2000), 541-569.
doi: 10.1007/s10107-006-0722-8.
|
[30]
|
D. Roman, G. Mitra and V. Zverovich, Enhanced indexation based on second-order stochastic dominance, European J. Oper. Res., 228 (2013), 273-281.
doi: 10.1016/j.ejor.2013.01.035.
|
[31]
|
G. Rudolf and A. Ruszczyński, Optimization problems with second order stochastic dominance constraints: Duality, compact formulations, and cut generation methods, SIAM J. Optim., 19 (2008), 1326-1343.
doi: 10.1137/070702473.
|
[32]
|
H. Sun, H. Xu and Y. Wang, A smoothing penalized sample average approximation method for stochastic programs with second order stochastic dominance constraints, Asia-Pac. J. Oper. Res., 30 (2013), 1340002 (25 pages).
doi: 10.1142/S0217595913400022.
|
[33]
|
H. Sun, H. Xu, R. Meskarian and Y. Wang, Exact penalization, level function method and modified cutting-plane method for stochastic programs with second order stochastic dominance constraints, SIAM J. Optim., 23 (2013), 602-631.
doi: 10.1137/110850815.
|
[34]
|
H. Sun and H. Xu, Convergence analysis of stationary points in-sample average approximation of stochastic programs with second order stochastic dominance constraints, Math. Program., 143 (2014), 31-59.
doi: 10.1007/s10107-013-0711-7.
|
[35]
|
W. E. Sharpe, The Sharpe Ratio, J. Portfolio Manage., 21 (1994), 49-58.
doi: 10.3905/jpm.1994.409501.
|
[36]
|
F. A. Sortino and L. N. Price, Performance measurement in a downside risk framework, J. Invest., 3 (2009), 59-64.
doi: 10.3905/joi.3.3.59.
|
[37]
|
G. A. Whitmore and M. C. Findlay, (eds.), Stochastic Dominance: An Approach to Decision-Making Under Risk, D.C.Heath, Lexington, MA., 1978.
|
[38]
|
F. Xu, M. Wang, Y. H. Dai and D. Xu, A sparse enhanced indexation model with chance and cardinality constraints, J. Glob. Optim., 70 (2018), 5-25.
doi: 10.1007/s10898-017-0513-1.
|