Scenario Generation for Single-Period Portfolio Selection Problems with Tail Risk Measures: Coping with High Dimensions and Integer Variables
Published Online:21 Sep 2018https://doi.org/10.1287/ijoc.2017.0790
References
- (2002) On the coherence of expected shortfall. J. Banking Finance 26(7):1487–1503.Crossref, Google Scholar
- (1999) Coherent measures of risk. Math. Finance 9(3):203–228.Crossref, Google Scholar
- (2003) Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. J. Roy. Statist. Soc. Ser. B 65(2):367–389.Crossref, Google Scholar
- (2006) Assessing solution quality in stochastic programs. Math. Programming 108(2–3):495–514.Crossref, Google Scholar
- (2006) Robust and data-driven optimization: Modern decision making under uncertainty. Johnson MP, Norman B, Secomandi N, eds. Models, Methods, and Applications for Innovative Decision Making. INFORMS Tutorials in Operations Research (INFORMS, Catonsville, MD), 95–122.Link, Google Scholar
- (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
- (1965) Algorithm for finding a general formula for the non-negative solutions of a system of linear inequalities. U.S.S.R. Comput. Math. Math. Phys. 5(2):228–233.Crossref, Google Scholar
- (1992) The Linear Complementarity Problem, Classics in Applied Mathematics, Vol. 60 (SIAM, Philadelphia).Google Scholar
- (1999) The practice of portfolio replication. A practical overview of forward and inverse problems. Ann. Oper. Res. 85:267–284.Crossref, Google Scholar
- (2016) Problem-Driven Scenario Generation. PhD thesis, Lancaster University, Lancashire, UK.Google Scholar
- (2017a) Distributions modelling FTSE100 stock returns. Accessed February 15, 2018, https://dx.doi.org/10.17635/lancaster/researchdata/158.Google Scholar
- (2017b) TailRiskScenGen.jl: Julia package for scenario generation for stochastic programs with tail risk measure. Accessed February 15, 2018, https://github.com/STOR-i/TailRiskScenGen.jl.Google Scholar
- (2017) Problem-driven scenario generation: An analytical approach to stochastic programs with tail risk measure. Accessed February 15, 2018, http://arxiv.org/abs/1511.03074.Google Scholar
- (1989) Symmetric Multivariate and Related Distributions (Chapman & Hall/CRC Monographs on Statistics & Applied Probability) (Chapman and Hall/CRC, Boca Raton, FL).Google Scholar
- (2003) A heuristic for moment-matching scenario generation. Comput. Optim. Appl. 24(2–3):169–185.Crossref, Google Scholar
- (2010) Portfolio selection under distributional uncertainty: A relative robust {CVaR} approach. Eur. J. Oper. Res. 203(1):185–194.Crossref, Google Scholar
- (1996) Value at Risk: The New Benchmark for Controlling Market Risk (Irwin Professional, Burr Ridge, IL).Google Scholar
- (2007) Evaluation of scenario-generation methods for stochastic programming. Pacific J. Optim. 3(2):257–271.Google Scholar
- (2007) Stability analysis of portfolio management with conditional value-at-risk. Quant. Finance 7(4):397–409.Crossref, Google Scholar
- (2001) The sample average approximation method for stochastic discrete optimization. SIAM J. Optim. 12(2):479–502.Crossref, Google Scholar
- (1992) A note on Chernikova’s algorithm. Technical Report 635, IRISA, Rennes, France.Google Scholar
- (2007) Portfolio optimization with linear and fixed transaction costs. Ann. Oper. Res. 152(1):341–365.Crossref, Google Scholar
- (1952) Portfolio selection. J. Finance 7(1):77–91.Google Scholar
- (1959) Portfolio Selection: Efficient Diversification of Investment (Yale University Press, New Haven, CT).Google Scholar
- (2000) Optimization of conditional value-at-risk. J. Risk 2(3):21–41.Crossref, Google Scholar
- (2013) Optimal budget allocation for sample average approximation. Oper. Res. 61(3):762–776.Link, Google Scholar
- (2013) A probability metrics approach for reducing the bias of optimality gap estimators in two-stage stochastic linear programming. Math. Programming 142(1–2):107–131.Crossref, Google Scholar
- (2002) Expected shortfall and beyond. J. Banking Finance 26(7):1519–1533.Crossref, Google Scholar
- (1998) A minimax portfolio selection rule with linear programming solution. Management Sci. 44(5):673–683.Link, Google Scholar
- (2008) Lectures on Polytopes. Graduate Texts in Mathematics, Vol. 152 (Springer, New York).Google Scholar

