An Efficient Scenario Reduction Method for Problems with Higher Moment Coherent Risk Measures

References

• Aksaraylı M, Pala O (2018) A polynomial goal programming model for portfolio optimization based on entropy and higher moments. Expert Systems Appl. 94:185–192.Crossref, Google Scholar
• Arpón S, Homem-de Mello T, Pagnoncelli B (2018) Scenario reduction for stochastic programs with conditional value-at-risk. Math. Programming 170(1):327–356.Crossref, Google Scholar
• Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math. Finance 9(3):203–228.Crossref, Google Scholar
• Beltran F, de Oliveira W, Finardi EC (2017) Application of scenario tree reduction via quadratic process to medium-term hydrothermal scheduling problem. IEEE Trans. Power Systems 32(6):4351–4361.Crossref, Google Scholar
• Ben-Tal A, Teboulle M (1986) Expected utility, penalty functions, and duality in stochastic nonlinear programming. Management Sci. 32(11):1445–1466.Link, Google Scholar
• Ben-Tal A, Teboulle M (2007) An old-new concept of convex risk measures: The optimized certainty equivalent. Math. Finance 17(3):449–476.Crossref, Google Scholar
• Chen Z, Yan Z (2018) Scenario tree reduction methods through clustering nodes. Comput. Chemical Engrg. 109:96–111.Crossref, Google Scholar
• Delbaen F (2002) Coherent risk measures on general probability spaces. Sandman K, Schönbucher PJ, eds. Advances in Finance and Stochastics (Springer, Berlin), 1–37.Crossref, Google Scholar
• Dupačová J, Gröwe-Kuska N, Römisch W (2003) Scenario reduction in stochastic programming. Math. Programming 95(3):493–511.Crossref, Google Scholar
• Fairbrother A, Turner A, Wallace SW (2018) Scenario generation for single-period portfolio selection problems with tail risk measures: Coping with high dimensions and integer variables. INFORMS J. Comput. 30(3):472–491.Link, Google Scholar
• Fairbrother J, Turner A, Wallace SW (2022) Problem-driven scenario generation: An analytical approach for stochastic programs with tail risk measure. Math. Programming 191:141–182.Crossref, Google Scholar
• Feng Y, Ryan SM (2013) Scenario construction and reduction applied to stochastic power generation expansion planning. Comput. Oper. Res. 40(1):9–23.Crossref, Google Scholar
• Gao J, Li D (2013) Optimal cardinality constrained portfolio selection. Oper. Res. 61(3):745–761.Link, Google Scholar
• He X, Zhang W (2023) Two-stage international portfolio models with higher moment risk measures. Comput. Oper. Res. 154:106200.Crossref, Google Scholar
• He X, Zhang W (2024) An efficient scenario reduction method for problems with higher moment coherent risk measures. http://dx.doi.org/10.1287/ijoc.2022.0375.cd, https://github.com/INFORMSJoC/2022.0375.Google Scholar
• Heitsch H, Römisch W (2003) Scenario reduction algorithms in stochastic programming. Comput. Optim. Appl. 24(2–3):187–206.Crossref, Google Scholar
• Heitsch H, Römisch W (2007) A note on scenario reduction for two-stage stochastic programs. Oper. Res. Lett. 35(6):731–738.Crossref, Google Scholar
• Hitaj A, Zambruno G (2018) Portfolio optimization using modified Herfindahl constraint. Consigli G, Stefani S, Zambruno G, eds. Handbook of Recent Advances in Commodity and Financial Modeling: Quantitative Methods in Banking, Finance, Insurance, Energy and Commodity Markets (Springer International Publishing, Cham, Switzerland), 211–239.Crossref, Google Scholar
• Hu J, Li H (2019) A new clustering approach for scenario reduction in multi-stochastic variable programming. IEEE Trans. Power Systems 34(5):3813–3825.Crossref, Google Scholar
• Hu J, Li H, Liu Z (2021) Scenario reduction based on correlation sensitivity and its application in microgrid optimization. Internat. Trans. Electr. Energy Systems 31(3):e12747.Google Scholar
• Kalayci CB, Polat O, Akbay MA (2020) An efficient hybrid metaheuristic algorithm for cardinality constrained portfolio optimization. Swarm Evolutionary Comput. 54:100662.Crossref, Google Scholar
• Kovacevic R, Pichler A (2015) Tree approximation for discrete time stochastic processes: A process distance approach. Ann. Oper. Res. 235(1):395–421.Crossref, Google Scholar
• Krokhmal PA (2007) Higher moment coherent risk measures. Quant. Finance 7(4):373–387.Crossref, Google Scholar
• Krokhmal P, Zabarankin M, Uryasev S (2011) Modeling and optimization of risk. Surveys Oper. Res. Management Sci. 16(2):49–66.Crossref, Google Scholar
• Latorre JM, Cerisola S, Ramos A (2007) Clustering algorithms for scenario tree generation: Application to natural hydro inflows. Eur. J. Oper. Res. 181(3):1339–1353.Crossref, Google Scholar
• Li Z, Floudas CA (2014) Optimal scenario reduction framework based on distance of uncertainty distribution and output performance: I. Single reduction via mixed integer linear optimization. Comput. Chemical Engrg. 70:50–66.Crossref, Google Scholar
• Li Z, Floudas CA (2016) Optimal scenario reduction framework based on distance of uncertainty distribution and output performance: II. Sequential reduction. Comput. Chemical Engrg. 84:599–610.Crossref, Google Scholar
• Li Z, Li Z (2016) Linear programming-based scenario reduction using transportation distance. Comput. Chemical Engrg. 88:50–58.Crossref, Google Scholar
• Liu W, Yang L, Yu B (2021) KDE distributionally robust portfolio optimization with higher moment coherent risk. Ann. Oper. Res. 307(1):363–397.Crossref, Google Scholar
• Matmoura Y, Penev S (2013) Multistage optimization of option portfolio using higher order coherent risk measures. Eur. J. Oper. Res. 227(1):190–198.Crossref, Google Scholar
• Pflug GC (2009) Version-independence and nested distributions in multistage stochastic optimization. SIAM J. Optim. 20(3):1406–1420.Crossref, Google Scholar
• Pflug GC, Pichler A (2012) A distance for multistage stochastic optimization models. SIAM J. Optim. 22(1):1–23.Crossref, Google Scholar
• Pflug GC, Pichler A (2015) Dynamic generation of scenario trees. Comput. Optim. Appl. 62(3):641–668.Crossref, Google Scholar
• Pineda S, Conejo A (2010) Scenario reduction for risk-averse electricity trading. IET Generation Transmission Distribution 4(6):694–705.Crossref, Google Scholar
• Post T, Potì V (2017) Portfolio analysis using stochastic dominance, relative entropy, and empirical likelihood. Management Sci. 63(1):153–165.Link, Google Scholar
• Rahimian H, Bayraksan G, Homem-de Mello T (2019) Identifying effective scenarios in distributionally robust stochastic programs with total variation distance. Math. Programming 173(1):393–430.Crossref, Google Scholar
• Rockafellar RT, Uryasev S (2013) The fundamental risk quadrangle in risk management, optimization and statistical estimation. Surveys Oper. Res. Management Sci. 18(1):33–53.Google Scholar
• Rockafellar RT, Wets RJB (1998) Variational Analysis (Springer, Berlin), 238–297.Crossref, Google Scholar
• Rysz M, Vinel A, Krokhmal P, Pasiliao EL (2015) A scenario decomposition algorithm for stochastic programming problems with a class of downside risk measures. INFORMS J. Comput. 27(2):416–430.Link, Google Scholar
• Sahinidis NV (2004) Optimization under uncertainty: State-of-the-art and opportunities. Comput. Chemical Engrg. 28(6):971–983.Crossref, Google Scholar
• Saranya K, Prasanna PK (2014) Portfolio selection and optimization with higher moments: Evidence from the Indian stock market. Asia Pacific Financial Markets 21(2):133–149.Crossref, Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński A (2014) Lectures on Stochastic Programming: Modeling and Theory, 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia).Crossref, Google Scholar
• Topaloglou N, Vladimirou H, Zenios SA (2020) Integrated dynamic models for hedging international portfolio risks. Eur. J. Oper. Res. 285(1):48–65.Crossref, Google Scholar
• Vinel A, Krokhmal PA (2017) Certainty equivalent measures of risk. Ann. Oper. Res. 249:75–95.Crossref, Google Scholar
• Wang Y, Liu Y, Kirschen DS (2017) Scenario reduction with submodular optimization. IEEE Trans. Power Systems 32(3):2479–2480.Crossref, Google Scholar
• Woerheide W, Persson D (1992) An index of portfolio diversification. Financial Services Rev. 2(2):73–85.Crossref, Google Scholar
• Xu D, Chen Z, Yang L (2012) Scenario tree generation approaches using K-means and LP moment matching methods. J. Comput. Appl. Math. 236(17):4561–4579.Crossref, Google Scholar