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Simulation of Lévy-Driven models and its application in finance
A survey on probabilistically constrained optimization problems
1. | School of Management, Fudan University, Shanghai 200433, China |
2. | School of Economics and Management, Tongji University, Shanghai 200092, China |
References:
[1] |
G. J. Alexander and A. M. Baptista, A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model, Management Science, 50 (2004), 1261-1273.
doi: 10.1287/mnsc.1040.0201. |
[2] |
G. J. Alexander, A. M. Baptista and S. Yan, Mean-variance portfolio selection with 'at-risk' constraints and discrete distributions, Journal of Banking & Finance, 31 (2007), 3761-3781.
doi: 10.1016/j.jbankfin.2007.01.019. |
[3] |
X. D. Bai, J. Sun, X. J. Zheng and X. L. Sun, A penalty decomposition method for probabilistically constrained convex programs, Technical report, School of Management, Fudan University, P. R. China, 2012. Available from: http://www.optimization-online.org/DB_HTML/2012/04/3448.html. |
[4] |
A. Ben-Tal, L. El Ghaoui and A. S. Nemirovski, "Robust Optimization," Princeton University Press, 2009. |
[5] |
S. Benati and R. Rizzi, A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem, European Journal of Operational Research, 176 (2007), 423-434.
doi: 10.1016/j.ejor.2005.07.020. |
[6] |
P. Beraldi and A. Ruszczyński, The probabilistic set-covering problem, Operations Research, 50 (2002), 956-967.
doi: 10.1287/opre.50.6.956.345. |
[7] |
P. Bonami and M. A. Lejeune, An exact solution approach for portfolio optimization problems under stochastic and integer constraints, Operations Research, 57 (2009), 650-670.
doi: 10.1287/opre.1080.0599. |
[8] |
S. P. Boyd and L. Vandenberghe, "Convex Optimization," Cambridge University Press, 2004. |
[9] |
G. C. Calafiore and M. C. Campi, The scenario approach to robust control design, IEEE Transactions on Automatic Control, 51 (2006), 742-753.
doi: 10.1109/TAC.2006.875041. |
[10] |
A. Charnes and W. W. Cooper, Chance-constrained programming, Management Science, 6 (1959), 73-79.
doi: 10.1287/mnsc.6.1.73. |
[11] |
W. Chen, M. Sim, J. Sun and C. P. Teo, From CVaR to uncertainty set: Implications in joint chance-constrained optimization, Operations Research, 58 (2010), 470-485.
doi: [10.1287/opre.1090.0712. |
[12] |
M. S. Cheon, S. Ahmed and F. Al-Khayyal, A branch-reduce-cut algorithm for the global optimization of probabilistically constrained linear programs, Mathematical Programming, 108 (2006), 617-634.
doi: 10.1007/s10107-006-0725-5. |
[13] |
D. Dentcheva and G. Martinez, Augmented Lagrangian method for probabilistic optimization, Annals of Operations Research, 200 (2012), 109-130.
doi: 10.1007/s10479-011-0884-5. |
[14] |
D. Dentcheva, A. Prékopa and A. Ruszczynski, Concavity and efficient points of discrete distributions in probabilistic programming, Mathematical Programming, 89 (2000), 55-77.
doi: 10.1007/PL00011393. |
[15] |
A. A. Gaivoronski and G. Pflug, Value at risk in portfolio optimization: Properties and computational approach, Journal of Risk, 7 (2005), 1-31. |
[16] |
R. Henrion, Structural properties of linear probabilistic constraints, Optimization, 56 (2007), 425-440.
doi: 10.1080/02331930701421046. |
[17] |
R. Henrion and C. Strugarek, Convexity of chance constraints with independent random variables, Computational Optimization and Applications, 41 (2008), 263-276.
doi: 10.1007/s10589-007-9105-1. |
[18] |
L. J. Hong, Y. Yang, and L. Zhang, Sequential convex approximations to joint chance constrained programs: A monte carlo approach, Operations Research, 59 (2011), 617-630.
doi: 10.1287/opre.1100.0910. |
[19] |
S. Küçükyavuz, On mixing sets arising in chance-constrained programming, Mathematical Programming, 132 (2012), 31-56.
doi: 10.1007/s10107-010-0385-3. |
[20] |
C. M. Lagoa, X. Li, and M. Sznaier, Probabilistically constrained linear programs and risk-adjusted controller design, SIAM Journal on Optimization, 15 (2005), 938-951.
doi: 10.1137/S1052623403430099. |
[21] |
M. Lejeune and N. Noyan, Mathematical programming approaches for generating p-efficient points, European Journal of Operational Research, 207 (2010), 590-600.
doi: 10.1016/j.ejor.2010.05.025. |
[22] |
M. A. Lejeune and A. Ruszczynski, An efficient trajectory method for probabilistic inventory production-distribution problems, Operations Research, 55 (2007), 378-394.
doi: 10.1287/opre.1060.0356. |
[23] |
J. Luedtke and S. Ahmed, A sample approximation approach for optimization with probabilistic constraints, SIAM Journal on Optimization, 19 (2008), 674-699.
doi: 10.1137/070702928. |
[24] |
J. Luedtke, S. Ahmed and G. L. Nemhauser, An integer programming approach for linear programs with probabilistic constraints, Mathematical Programming, 122 (2010), 247-272.
doi: 10.1007/s10107-008-0247-4. |
[25] |
A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs, SIAM Journal on Optimization, 17 (2006), 969-996.
doi: 10.1137/050622328. |
[26] |
A. Nemirovski and A. Shapiro, Scenario approximations of chance constraints, in "Probabilistic and Randomized Methods for Design Under Uncertainty" (eds. G. Calafiore and F. Dabbene), Springer, (2006), 3-47.
doi: 10.1007/1-84628-095-8_1. |
[27] |
J. Nocedal and S. J. Wright, "Numerical Optimization," Springer, 1999.
doi: 10.1007/b98874. |
[28] |
A. Prékopa, Probabilistic programming, in "Stochastic Programming, " Handbooks in Operations Research and Management Science (eds. A. Ruszczyński and A. Shapiro), Elsevier, (2003), 267-351. |
[29] |
R. T. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk, Journal of Risk, 2 (2000), 21-42. |
[30] |
A. Ruszczyński, Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra, Mathematical Programming, 93 (2002), 195-215.
doi: 10.1007/s10107-002-0337-7. |
[31] |
A. Saxena, V. Goyal and M. A. Lejeune, MIP reformulations of the probabilistic set covering problem, Mathematical Programming, 121 (2010), 1-31.
doi: 10.1007/s10107-008-0224-y. |
[32] |
X. J. Zheng, X. L. Sun, D. Li and X. T. Cui, Lagrangian decomposition and mixed-integer quadratic programming reformulations for probabilistically constrained quadratic programs, European Journal of Operational Research, 221 (2012), 38-48.
doi: 10.1016/j.ejor.2012.03.006. |
show all references
References:
[1] |
G. J. Alexander and A. M. Baptista, A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model, Management Science, 50 (2004), 1261-1273.
doi: 10.1287/mnsc.1040.0201. |
[2] |
G. J. Alexander, A. M. Baptista and S. Yan, Mean-variance portfolio selection with 'at-risk' constraints and discrete distributions, Journal of Banking & Finance, 31 (2007), 3761-3781.
doi: 10.1016/j.jbankfin.2007.01.019. |
[3] |
X. D. Bai, J. Sun, X. J. Zheng and X. L. Sun, A penalty decomposition method for probabilistically constrained convex programs, Technical report, School of Management, Fudan University, P. R. China, 2012. Available from: http://www.optimization-online.org/DB_HTML/2012/04/3448.html. |
[4] |
A. Ben-Tal, L. El Ghaoui and A. S. Nemirovski, "Robust Optimization," Princeton University Press, 2009. |
[5] |
S. Benati and R. Rizzi, A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem, European Journal of Operational Research, 176 (2007), 423-434.
doi: 10.1016/j.ejor.2005.07.020. |
[6] |
P. Beraldi and A. Ruszczyński, The probabilistic set-covering problem, Operations Research, 50 (2002), 956-967.
doi: 10.1287/opre.50.6.956.345. |
[7] |
P. Bonami and M. A. Lejeune, An exact solution approach for portfolio optimization problems under stochastic and integer constraints, Operations Research, 57 (2009), 650-670.
doi: 10.1287/opre.1080.0599. |
[8] |
S. P. Boyd and L. Vandenberghe, "Convex Optimization," Cambridge University Press, 2004. |
[9] |
G. C. Calafiore and M. C. Campi, The scenario approach to robust control design, IEEE Transactions on Automatic Control, 51 (2006), 742-753.
doi: 10.1109/TAC.2006.875041. |
[10] |
A. Charnes and W. W. Cooper, Chance-constrained programming, Management Science, 6 (1959), 73-79.
doi: 10.1287/mnsc.6.1.73. |
[11] |
W. Chen, M. Sim, J. Sun and C. P. Teo, From CVaR to uncertainty set: Implications in joint chance-constrained optimization, Operations Research, 58 (2010), 470-485.
doi: [10.1287/opre.1090.0712. |
[12] |
M. S. Cheon, S. Ahmed and F. Al-Khayyal, A branch-reduce-cut algorithm for the global optimization of probabilistically constrained linear programs, Mathematical Programming, 108 (2006), 617-634.
doi: 10.1007/s10107-006-0725-5. |
[13] |
D. Dentcheva and G. Martinez, Augmented Lagrangian method for probabilistic optimization, Annals of Operations Research, 200 (2012), 109-130.
doi: 10.1007/s10479-011-0884-5. |
[14] |
D. Dentcheva, A. Prékopa and A. Ruszczynski, Concavity and efficient points of discrete distributions in probabilistic programming, Mathematical Programming, 89 (2000), 55-77.
doi: 10.1007/PL00011393. |
[15] |
A. A. Gaivoronski and G. Pflug, Value at risk in portfolio optimization: Properties and computational approach, Journal of Risk, 7 (2005), 1-31. |
[16] |
R. Henrion, Structural properties of linear probabilistic constraints, Optimization, 56 (2007), 425-440.
doi: 10.1080/02331930701421046. |
[17] |
R. Henrion and C. Strugarek, Convexity of chance constraints with independent random variables, Computational Optimization and Applications, 41 (2008), 263-276.
doi: 10.1007/s10589-007-9105-1. |
[18] |
L. J. Hong, Y. Yang, and L. Zhang, Sequential convex approximations to joint chance constrained programs: A monte carlo approach, Operations Research, 59 (2011), 617-630.
doi: 10.1287/opre.1100.0910. |
[19] |
S. Küçükyavuz, On mixing sets arising in chance-constrained programming, Mathematical Programming, 132 (2012), 31-56.
doi: 10.1007/s10107-010-0385-3. |
[20] |
C. M. Lagoa, X. Li, and M. Sznaier, Probabilistically constrained linear programs and risk-adjusted controller design, SIAM Journal on Optimization, 15 (2005), 938-951.
doi: 10.1137/S1052623403430099. |
[21] |
M. Lejeune and N. Noyan, Mathematical programming approaches for generating p-efficient points, European Journal of Operational Research, 207 (2010), 590-600.
doi: 10.1016/j.ejor.2010.05.025. |
[22] |
M. A. Lejeune and A. Ruszczynski, An efficient trajectory method for probabilistic inventory production-distribution problems, Operations Research, 55 (2007), 378-394.
doi: 10.1287/opre.1060.0356. |
[23] |
J. Luedtke and S. Ahmed, A sample approximation approach for optimization with probabilistic constraints, SIAM Journal on Optimization, 19 (2008), 674-699.
doi: 10.1137/070702928. |
[24] |
J. Luedtke, S. Ahmed and G. L. Nemhauser, An integer programming approach for linear programs with probabilistic constraints, Mathematical Programming, 122 (2010), 247-272.
doi: 10.1007/s10107-008-0247-4. |
[25] |
A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs, SIAM Journal on Optimization, 17 (2006), 969-996.
doi: 10.1137/050622328. |
[26] |
A. Nemirovski and A. Shapiro, Scenario approximations of chance constraints, in "Probabilistic and Randomized Methods for Design Under Uncertainty" (eds. G. Calafiore and F. Dabbene), Springer, (2006), 3-47.
doi: 10.1007/1-84628-095-8_1. |
[27] |
J. Nocedal and S. J. Wright, "Numerical Optimization," Springer, 1999.
doi: 10.1007/b98874. |
[28] |
A. Prékopa, Probabilistic programming, in "Stochastic Programming, " Handbooks in Operations Research and Management Science (eds. A. Ruszczyński and A. Shapiro), Elsevier, (2003), 267-351. |
[29] |
R. T. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk, Journal of Risk, 2 (2000), 21-42. |
[30] |
A. Ruszczyński, Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra, Mathematical Programming, 93 (2002), 195-215.
doi: 10.1007/s10107-002-0337-7. |
[31] |
A. Saxena, V. Goyal and M. A. Lejeune, MIP reformulations of the probabilistic set covering problem, Mathematical Programming, 121 (2010), 1-31.
doi: 10.1007/s10107-008-0224-y. |
[32] |
X. J. Zheng, X. L. Sun, D. Li and X. T. Cui, Lagrangian decomposition and mixed-integer quadratic programming reformulations for probabilistically constrained quadratic programs, European Journal of Operational Research, 221 (2012), 38-48.
doi: 10.1016/j.ejor.2012.03.006. |
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