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Robust and Reliable Portfolio Optimization Formulation of a Chance Constrained Problem

Foundations of Computing and Decision Sciences
Volume 42 (2017): Issue 1 (February 2017)
By:
Open Access
|Mar 2017

References

  1. [1] Adida, E. and Perakis, G., A robust optimization approach to dynamic pricing and inventory control with no backorders. Mathematical Programming, 107, 2006, 97-129.10.1007/s10107-005-0681-5
    Search in Google ScholarBack to article
  2. [2] Atamtäurk, A., Strong formulations of Robust Mixed 0-1 programming. Mathematical Programming: Series (B), 108, 2006, 235-250.10.1007/s10107-006-0709-5
    Search in Google ScholarBack to article
  3. [3] Atamtäurk, A. and Zhang, M., Two-stage Robust Network flow and Design under Demand Uncertainty. Operations Research, 55, 2007, 662-673.10.1287/opre.1070.0428
    Search in Google ScholarBack to article
  4. [4] Ben-Tal, A., Bertsimas, D. and Brown, D. B., A Soft Robust Model for Optimization under Ambiguity. Operations Research, 58, 2010, 1220-1234.10.1287/opre.1100.0821
    Search in Google ScholarBack to article
  5. [5] Ben-Tal, A., Boyd, S. and Nemirovski, A., Extending the scope of robust optimization. Mathematical Programming: Series (B), 107, 2006, 63-89.10.1007/s10107-005-0679-z
    Search in Google ScholarBack to article
  6. [6] Ben-Tal, A., El Ghaoui, L. and Nemirovski, A., Robust semidefinite programming in Semi-definite programming and applications, R. Saigal, Vandenberghe, H. Wolkowicz (Edited), Kluwer Academic Publishers, 2000a.
    Search in Google ScholarBack to article
  7. [7] Ben-Tal, A., El-Ghaoui, L. and Nemirovski, A., Robust optimization: Princeton Series in Applied Mathematics. Princeton University Press, Princeton, NJ, 2009.10.1515/9781400831050
    Search in Google ScholarBack to article
  8. [8] Ben-Tal, A., Golany, B., Nemirovski, A. and Vial, J. P., Supplier-retailer flexible commitments contracts: A Robust Optimization Approach. Manufacturing and Service Operations Management, 7, 2005, 248-271.10.1287/msom.1050.0081
    Search in Google ScholarBack to article
  9. [9] Ben-Tal, A., Goryashko, A., Guslitzer, E. and Nemirovski, A., Adjustable Robust solutions of uncertain linear Programs. Mathematical Programming, 99, 2004, 351-376.10.1007/s10107-003-0454-y
    Search in Google ScholarBack to article
  10. [10] Ben-Tal, A., Margalit, T. and Nemirovski, A., Robust modeling of multi-stage portfolio problems; High Performance Optimization, Frenk, H., Roos, C., Terlaky, T., Zhang, S. (Edited), Kluwer Academic Publishers, 2000b, 303–328.10.1007/978-1-4757-3216-0_12
    Search in Google ScholarBack to article
  11. [11] Ben-Tal, A. and Nemirovski, A., Robust truss topology design via semi-definite programming. SIAM Journal on Optimization, 7, 1997, 991-1016.10.1137/S1052623495291951
    Search in Google ScholarBack to article
  12. [12] Ben-Tal, A. and Nemirovski, A., Robust convex optimization. Mathematics of Operations Research,23, 1998, 769-805.10.1287/moor.23.4.769
    Search in Google ScholarBack to article
  13. [13] Ben-Tal, A. and Nemirovski., A, Robust solutions to uncertain linear programs. Operations Research Letters, 25, 1999, 1–13.10.1016/S0167-6377(99)00016-4
    Search in Google ScholarBack to article
  14. [14] Ben-Tal, A. and Nemirovski, A., Robust solutions of Linear Programming problems contaminated with uncertain data. Mathematical Programming: Series (A). 88, 2000c, 411-424.10.1007/PL00011380
    Search in Google ScholarBack to article
  15. [15] Ben-Tal, A. and Nemirovski, A., Lectures on modern convex optimization: Analysis, algorithms and engineering applications, MPR-SIAM Series on Optimization, SIAM, Philadelphia, 2001a.10.1137/1.9780898718829
    Search in Google ScholarBack to article
  16. [16] Ben-Tal, A. and Nemirovski, A., On approximate Robust counterparts of uncertain semi-definite and conic quadratic programs. Proceedings of 20th IFIP TC7 Conference on System Modelling and Optimization, July 23-27, Trier, Germany, 2001b.
    Search in Google ScholarBack to article
  17. [17] Ben-Tal, A. and Nemirovski, A., Robust optimization–Methodology and Applications. Mathematical Programming: Series (B), 92, 2002a, 453-480.10.1007/s101070100286
    Search in Google ScholarBack to article
  18. [18] Ben-Tal, A. and Nemirovski, A., On tractable approximations of uncertain linear matrix inequalities affected by interval uncertainty. SIAM Journal on Optimization, 12, 2002b, 811-833.10.1137/S1052623400374756
    Search in Google ScholarBack to article
  19. [19] Ben-Tal, A., Nemirovski, A. and Roos, C., Robust solutions of uncertain quadratic and conic-quadratic problems. SIAM Journal on Optimization, 13, 2002c, 535-560.10.1137/S1052623401392354
    Search in Google ScholarBack to article
  20. [20] Bertsekas, D. P., Dynamic Programming and Optimal Control (Volume: I). Athena Scientific, Belmont, Massachusetts, USA, 1995.
    Search in Google ScholarBack to article
  21. [21] Bertsimas, D. and Caramanis, C., Finite adaptability in Multistage Linear Optimization. IEEE Transactions on Automatic Control, 55, 2007, 2751-2766.10.1109/TAC.2010.2049764
    Search in Google ScholarBack to article
  22. [22] Bertsimas, D. and Brown, David B., Constructing Uncertainty Sets for Robust Linear Optimization, Operations Research, 57, 2009, 1483-1495.10.1287/opre.1080.0646
    Search in Google ScholarBack to article
  23. [23] Bertsimas, D., Brown, D. B. and Caramanis, C., Theory and Applications of Robust Optimization. SIAM Review, 53, 2011, 464-501.10.1137/080734510
    Search in Google ScholarBack to article
  24. [24] Bertsimas, D., Nohadani, O. and Teo, K. M., Robust Optimization for Unconstrained Simulation-based Problems. Operations Research, 58, 2010, 161-178.10.1287/opre.1090.0715
    Search in Google ScholarBack to article
  25. [25] Bertsimas, D., Pachamanova, D. and Sim, M., Robust linear optimization under general norms. Operations Research Letters, 32, 2004, 510-516.10.1016/j.orl.2003.12.007
    Search in Google ScholarBack to article
  26. [26] Bertsimas, D. and Popescu, I., Optimal inequalities in probability theory: A convex optimization approach. SIAM Journal of Optimization, 15, 2004, 780-800.10.1137/S1052623401399903
    Search in Google ScholarBack to article
  27. [27] Bertsimas, D. and Sim, M., Robust discrete optimization and network flows. Mathematical Programming: Series: Series (B), 98, 2003, 49-71.10.1007/s10107-003-0396-4
    Search in Google ScholarBack to article
  28. [28] Bertsimas, D. and Sim, M., The price of robustness. Operations Research,52, 2004, 35-53.10.1287/opre.1030.0065
    Search in Google ScholarBack to article
  29. [29] Bertsimas, D. and Sim, M., Tractable approximations to robust conic optimization problems. Mathematical Programming: Series (B), 107, 2006, 5-36.10.1007/s10107-005-0677-1
    Search in Google ScholarBack to article
  30. [30] Bertsimas, D. and Thiele, A., A robust optimization approach to supply chain management. Operations Research, 54, 2006, 150-168.10.1287/opre.1050.0238
    Search in Google ScholarBack to article
  31. [31] Bertsimas, D. and Tsitsiklis, J., Introduction to Linear Optimization. Athena Scientific, 1997.
    Search in Google ScholarBack to article
  32. [32] Beyer, H-G. and Sendhoff, B., Robust optimization–A comprehensive survey. Computer Methods in Applied Mechanics and Engineering, 196, 2007, 3190-3128.10.1016/j.cma.2007.03.003
    Search in Google ScholarBack to article
  33. [33] Bienstock, D, Histogram models for robust portfolio optimization. Journal of Computational Finance, 11, 2007, 1-64.10.21314/JCF.2007.168
    Search in Google ScholarBack to article
  34. [34] Birge, J. R. and Louveaux, F., Introduction to Stochastic Programming. Springer-Verlag, 1997.
    Search in Google ScholarBack to article
  35. [35] Boyd, S., El Ghaoui, L., Feron, E. and Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory. SIAM, 1994.10.1137/1.9781611970777
    Search in Google ScholarBack to article
  36. [36] Boyd, S., Kim, S. J., Patil, D. and Horowitz, M., Digital circuit sizing via geometric programming. Operations Research, 53, 2005, 899-932.10.1287/opre.1050.0254
    Search in Google ScholarBack to article
  37. [37] Boyd, S. and Vandenberghe, L., Semidefinite programming. SIAM Review, 38, 1996, 49-95.10.1137/1038003
    Search in Google ScholarBack to article
  38. [38] Boyd, S. and Vandenberghe, L., Convex Optimization. Cambridge University Press, 2004.10.1017/CBO9780511804441
    Search in Google ScholarBack to article
  39. [39] Chen, W. and Sim, M., Goal Driven Optimization. Operations Research. 57, 2009, 342-357.10.1287/opre.1080.0570
    Search in Google ScholarBack to article
  40. [40] Chen, W., Sim, M., Sun, J. and Teo, Chung-Piaw, From CVaR to Uncertainty Set: Implications in Joint Chance Constrained Optimization, Operations Research, 58, 2010, 470-485.10.1287/opre.1090.0712
    Search in Google ScholarBack to article
  41. [41] Chen, X., Sim, M. and Sun, P., A robust optimization perspective to stochastic programming. Operations Research, 55, 2007, 1058-1071.10.1287/opre.1070.0441
    Search in Google ScholarBack to article
  42. [42] Chen, X., Sim, M., Sun, P. and Zhang, J., A linear-decision based approximation approach to stochastic programming. Operations Research, 56, 2008, 344-357.10.1287/opre.1070.0457
    Search in Google ScholarBack to article
  43. [43] Chen, X. and Zhang, Y., Uncertain Linear Programs: Extended Affinely Adjustable Robust Counterparts. Operations Research, 57, 2009, 1469-1482.10.1287/opre.1080.0605
    Search in Google ScholarBack to article
  44. [44] Dembo, R., Scenario optimization, Annals of Operations Research, 30, 1991, 63-80.10.1007/BF02204809
    Search in Google ScholarBack to article
  45. [45] Duzgun, R. and Thiele, A., Dynamic models of Robust optimization, in J. Cochran, editors, Encyclopedia of Operations Research and Management Science, Wiley, New York, 2011.10.1002/9780470400531.eorms0271
    Search in Google ScholarBack to article
  46. [46] El Ghaoui, L. and Lebret, H., Robust solutions to least-square problems with uncertain data matrices. SIAM Journal of Matrix Analysis and Applications, 18, 1997, 1035–1064.10.1137/S0895479896298130
    Search in Google ScholarBack to article
  47. [47] El Ghaoui, L., Oustry, F. and Lebret, H., Robust solutions to uncertain semi-definite programs. SIAM Journal on Optimization, 9, 1998, 33–52.10.1137/S1052623496305717
    Search in Google ScholarBack to article
  48. [48] El Ghaoui, L., Maksim Oks. and Oustry, F., Worst-Case Value-at-Risk and Robust Portfolio Optimization: A Conic Programming Approach. Operations Research, 51, 2003, 543-556.10.1287/opre.51.4.543.16101
    Search in Google ScholarBack to article
  49. [49] Fabozzi, Frank J., Huang, D. and Zhou, G., Robust portfolios: contributions from operations research and finance, Annals of Operations Research, 176, 2010, 191-220.10.1007/s10479-009-0515-6
    Search in Google ScholarBack to article
  50. [50] Fabozzi, Frank J., Kolm, P. N., Pachamanova, D. A. and Focardi, S. M, Robust Portfolio Optimization. Journal of Portfolio Management, 33, 2007, 40-48.10.3905/jpm.2007.684751
    Search in Google ScholarBack to article
  51. [51] Goldfarb, D. and Iyengar, G., Robust Portfolio Selection Problems. Mathematics of Operation Research, 28, 2003, 1-38.10.1287/moor.28.1.1.14260
    Search in Google ScholarBack to article
  52. [52] Gotoh, J, Shinozaki, K. and Takeda, A., Robust Portfolio Techniques for Mitigating the Fragility of CVaR Minimization and Generalization to Coherent Risk Measures, Quantitative Finance, 13, 2013, 1621-1635.10.1080/14697688.2012.738930
    Search in Google ScholarBack to article
  53. [53] Halldórsson, B. V. and Tütüncü, R. H., An interior-point method for a class of saddle point problems. Journal of Optimization Theory and Applications, 116, 2003, 559-590.10.1023/A:1023065319772
    Search in Google ScholarBack to article
  54. [54] Huang, D., Zhu, Shu-Shang., Fabozzi, Frank J. and Fukushima, M., Portfolio selection with uncertain exit time: A robust CVaR approach, Journal of Economic Dynamics and Control, 32, 2008, 594–623.10.1016/j.jedc.2007.03.003
    Search in Google ScholarBack to article
  55. [55] Iyengar, G., Robust dynamic programming. Mathematics of Operations Research, 30, 1994, 257-280.10.1287/moor.1040.0129
    Search in Google ScholarBack to article
  56. [56] Kall, P. and Wallace, S., Stochastic Programming. John Wiley & Sons, 1994.
    Search in Google ScholarBack to article
  57. [57] Kouvelis, P. and Yu, G., Robust discrete optimization and its applications. Kluwer Academic Publishers, Norwell, MA, 1997.10.1007/978-1-4757-2620-6
    Search in Google ScholarBack to article
  58. [58] Lahiri, S. N., On the moving block bootstrap under long range dependence, Statistics and Probability Letters.18, 1993, 405-413.10.1016/0167-7152(93)90035-H
    Search in Google ScholarBack to article
  59. [59] Lahiri, S. N., Resampling methods for dependent data, Springer, New York, 2003.10.1007/978-1-4757-3803-2
    Search in Google ScholarBack to article
  60. [60] Markowitz, H., Portfolio Selection, The Journal of Finance, 7, 1952, 77-91.10.1111/j.1540-6261.1952.tb01525.x
    Search in Google ScholarBack to article
  61. [61] Mulvey, J., Vanderbei, R. and Zenios, S., Robust optimization of large-scale systems. Operations Research, 43, 1995, 264-281.10.1287/opre.43.2.264
    Search in Google ScholarBack to article
  62. [62] Nemhauser, G. L. and Wolsey, L. A.,. Integer and Combinatorial Optimization. Wiley-Interscience Series in Dicrete Mathematics and Optimization, USA, 1988.10.1002/9781118627372
    Search in Google ScholarBack to article
  63. [63] Pinar, M. and Tütüncü, R., Robust profit opportunities in risky financial portfolios, Operations Research Letters, 33, 2005, 331-340.10.1016/j.orl.2004.08.005
    Search in Google ScholarBack to article
  64. [64] Prékopa, A., Stochastic Programming. Kluwer, 1995.10.1007/978-94-017-3087-7
    Search in Google ScholarBack to article
  65. [65] Shapiro, A., On complexity of multistage stochastic programs. Operations Research Letters, 34, 2006, 1-8.10.1016/j.orl.2005.02.003
    Search in Google ScholarBack to article
  66. [66] Sim, M. and Goh, J., Robust Optimization Made Easy with ROME. Operations Research, 59, 2011, 973-985.10.1287/opre.1110.0944
    Search in Google ScholarBack to article
  67. [67] Sniedovich, M., The art and science of modeling decision-making under severe uncertainty, Decision Making in Manufacturing and Services, 1, 2007, 111-136.10.7494/dmms.2007.1.2.111
    Search in Google ScholarBack to article
  68. [68] Soyster, A. L., Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research,21, 1973, 1154-1157.10.1287/opre.21.5.1154
    Search in Google ScholarBack to article
  69. [69] Tütüncü, R. H. and Koenig, M., Robust asset allocation. Annals of Operations Research, 132, 2004, 157-187.10.1023/B:ANOR.0000045281.41041.ed
    Search in Google ScholarBack to article
  70. [70] Zhou, K., Doyle, J. C. and Glove, K., Robust and Optimal Control. Prentice-Hall, NJ, 1996.
    Search in Google ScholarBack to article
  71. [71] Zhu, S. and Fukushima, M., Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management, Operations Research, 57, 2009, 1155-1168.10.1287/opre.1080.0684
    Search in Google ScholarBack to article
DOI: https://doi.org/10.1515/fcds-2017-0004 | Journal eISSN: 2300-3405 | Journal ISSN: 0867-6356
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Language: English
Page range: 83 - 117
Submitted on: May 31, 2015
Accepted on: Jan 23, 2016
Published on: Mar 4, 2017
Published by: Poznan University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Risk Management,
Investment Analysis,
Robust Optimization,
Conditional Value at Risk (CVaR),
Extreme Value Distribution
Related subjects:
Computer sciences,
Artificial intelligence,
Software development

© 2017 Raghu Nandan Sengupta, Rakesh Kumar, published by Poznan University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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