Abstract
This paper develops and tests a heuristic algorithm for scenario-based value-at-risk (VaR) optimization. Due to the high computational complexity of VaR optimization, conditional value-at-risk-based proxies are utilized for VaR objectives. It is shown that our heuristic algorithm obtains robust results with low computational complexity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
All optimizations are performed using IBM \(\hbox {CPLEX}^\circledR \) 12.3 solver on a server with 8 Quad-Core AMD Opteron Processors 8356 (32 cores in total) and 256Gb of RAM. Four threads are used for solving all problems and CPLEX parameters are left at their default values. The MIP solution time limit was set to 30 min.
References
Basel Committee on Banking Supervision. (2004). International convergence of capital measurement and capital standards (Tech. report). Basel: Bank for International Settlements.
Better, M., Glover, F., Kochenberger, G., & Wang, H. (2008). Simulation optimization: Applications in risk management. International Journal of Information Technology & Decision Making, 7(4), 571–587.
Brodie, J., Daubechies, I., De Mol, C., Giannone, D., & Loris, I. (2009). Sparse and stable Markowitz portfolios. Proceedings of the National Academy of Sciences of the USA, 106(30), 12267–12272.
Delage, E., & Ye, Y. (2010). Distributionally robust optimization under moment uncertainty with application to data-driven problems. Operations Research, 58(3), 595–612.
Gaivoronski, A. A., & Pflug, G. (2005). Value-at-risk in portfolio optimization: Properties and computational approach. Journal of Risk, 7(2), 1–31.
Gilli, M., Këllezi, E., & Hysi, H. (2006). A data-driven optimization heuristic for downside risk minimization. Journal of Risk, 8(3), 1–19.
Gotoh, J., & Takeda, A. (2011). On the role of norm constraints in portfolio selection. Computational Management Science, 8(4), 323–353.
Høyland, K., Kaut, M., & Wallace, S. W. (2003). A heuristic for moment-matching scenario generation. Computational Optimization and Applications, 24, 169–185.
Kang, Y., Batta, R., & Kwon, C. (2014). Value-at-risk model for hazardous material transportation. Annals of Operations Research, 222(1), 361–387.
Larsen, N., Mausser, H., & Uryasev, S. (2002). Algorithms for optimization of value-at-risk. In P. M. Pardalos & V. K. Tsitsiringos (Eds.), Financial Engineering, E-commerce and Supply Chain (pp. 129–157). Dordrecht: Kluwer Academic Publishers.
Mausser, H., & Romanko, O. (2012). Bias, exploitation and proxies in scenario-based risk minimization. Optimization, 61(10), 1191–1219.
Mausser, H., & Romanko, O. (2014). CVaR proxies for minimizing scenario-based value-at-risk. Journal of Industrial and Management Optimization, 10(4), 1109–1127.
Mausser, H., & Rosen, D. (1999). Efficient risk/return frontiers for credit risk. Algo Research Quarterly, 2(4), 35–48.
Natarajan, K., Pachamanova, D., & Sim, M. (2008). Incorporating asymmetric distributional information in robust value-at-risk optimization. Management Science, 54(3), 573–585.
Pagnoncelli, B.K., Ahmed, S., & Shapiro, A. (2008). Computational study of a chance constrained portfolio selection problem, Optimization Online. http://www.optimization-online.org/DB_FILE/2008/02/1899. Accessed 5 Feb 2015.
Pflug, G. C. (2000). Some remarks on the value-at-risk and the conditional value-at-risk. In S. Uryasev (Ed.), Probabilistic Constrained Optimization (pp. 272–281). Dordrecht: Kluwer Academic Publishers.
Quaranta, A. G., & Zaffaroni, A. (2008). Robust optimization of conditional value at risk and portfolio selection. Journal of Banking & Finance, 32(10), 2046–2056.
Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2, 21–41.
Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking and Finance, 26, 1443–1471.
Sarykalin, S., Serraino, G., & Uryasev, S. (2008). Value-at-risk vs. conditional value-at-risk in risk management and optimization. In Z. L. Chen & S. Raghavan (Eds.), Tutorials in Operations Research (pp. 270–294). Hanover, MD: INFORMS.
Uryasev, S., Theiler, U., & Serraino, G. (2010). Risk-return optimization with different risk-aggregation strategies. Journal of Risk Finance, 11(2), 129–146.
Wallace, S. W., & Ziemba, W. T. (Eds.). (2005). Applications of stochastic programming. MPS-SIAM series on pptimization, Philadelphia, PA: SIAM.
Wozabal, D. (2010). Value-at-risk optimization using the difference of convex algorithm. OR Spectrum (9 September 2010), 1–23. doi:10.1007/s00291-010-0225-0.
Wu, D., & Olson, D. (2010). Enterprise risk management: a DEA VaR approach in vendor selection. International Journal of Production Research, 48(16), 4919–4932.
Zhu, S., & Fukushima, M. (2009). Worst-case conditional value-at-risk with application to robust portfolio management. Operations Research, 57(5), 1155–1168.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Romanko, O., Mausser, H. Robust scenario-based value-at-risk optimization. Ann Oper Res 237, 203–218 (2016). https://doi.org/10.1007/s10479-015-1822-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-015-1822-8