Robustness to Dependency in Portfolio Optimization Using Overlapping Marginals

Published Online:https://doi.org/10.1287/opre.2015.1424

References

  • Beasley JE (1990) OR-library: Distributing test problems by electronic mail. J. Oper. Res. Soc. 41(11):1069–1072.CrossrefGoogle Scholar
  • Beeri C, Fagin R, Maier D, Yannakakis M (1983) On the desirability of acyclic database schemes. J. Assoc. Comput. Machinery 30(3): 479–513.CrossrefGoogle Scholar
  • Berge C (1976) Graphs and Hypergraphs (North-Holland, Amsterdam).Google Scholar
  • Bertsimas D, Natarajan K, Teo CP (2006) Persistence in discrete optimization under data uncertainty. Math. Programming, Series B 108(2–3): 251–274.CrossrefGoogle Scholar
  • Canakgoz NA, Beasley JE (2009) Mixed-integer programming approaches for index tracking and enhanced indexation. Eur. J. Oper. Res. 196(1): 384–399.CrossrefGoogle Scholar
  • Chow CK, Liu CN (1968) Approximating discrete probability distributions with dependence trees. IEEE Trans. Inform. Theory 14(3):462–467.CrossrefGoogle Scholar
  • CVX Research Inc (2012) CVX: Matlab software for disciplined convex programming, version 2.0 beta. http://cvxr.com/cvx.Google Scholar
  • Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3):595–612.LinkGoogle Scholar
  • Denuit M, Genest C, Marceau E (1999) Stochastic bounds on sums of dependent risks. Insurance: Math. Econom. 25(1):85–104.CrossrefGoogle Scholar
  • Doan XV, Natarajan K (2012) On the complexity of nonoverlapping multivariate marginal bounds for probabilistic combinatorial optimization problems. Oper. Res. 60(1):138–149.LinkGoogle Scholar
  • Dunham M, Murphy K (2012) PMTK3: Probabilistic modeling toolkit for Matlab/Octave, version 3. https://code.google.com/p/pmtk3/.Google Scholar
  • El Ghaoui L, Oks M, Oustry F (2003) Worst-case value-at-risk and robust portfolio optimization: A conic programming approach. Oper. Res. 51(4):543–556.LinkGoogle Scholar
  • Embrechts P, Puccetti G (2006) Bounds for functions of dependent risks. Finance and Stochastics 10(3):341–352.CrossrefGoogle Scholar
  • Embrechts P, Puccetti G (2010) Bounds for the sum of dependent risks having overlapping marginals. J. Multivariate Anal. 101(1):177–190.CrossrefGoogle Scholar
  • Embrechts P, Höing A, Juri A (2003) Using copulae to bound the value-at-risk for functions of dependent risks. Finance and Stochastics 7(2):145–167.CrossrefGoogle Scholar
  • Embrechts P, McNeil A, Straumann D (2002) Correlation and dependence in risk management: Properties and pitfalls. Dempster MAH, ed. Risk Management: Value at Risk and Beyond (Cambridge University Press, Cambridge, UK), 176–223.CrossrefGoogle Scholar
  • Fréchet M (1940) Les probabilités associées à un système d’événements compatibles et dépendants. I. Evenements en nombre fini fixe, Actualités Sci. Ind., n. 859 (Hermann et Cie, Paris).Google Scholar
  • Fréchet M (1951) Sur les tableaux de corrélation dont les marges sont données. Annales de l’Université de Lyon, Section A, Series 3 14: 53–77.Google Scholar
  • French K, Fama E (2013) Fama and French data library. Accessed December 2014, http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.Google Scholar
  • Garlappi L, Uppal R, Wang T (2007) Portfolio selection with parameter and model uncertainty: A multi-prior approach. Rev. Financial Stud. 20(7):41–81.CrossrefGoogle Scholar
  • Honeyman P, Lander RE, Yannakakis M (1980) Testing the universal instance assumption. Inform. Processing Lett. 10(1):14–19.CrossrefGoogle Scholar
  • Huang C, Darwiche A (1996) Inference in belief networks: A procedural guide. Internat. J. Approximate Reasoning 15(3):225–263.CrossrefGoogle Scholar
  • Jiroušek R (1991) Solution of the marginal problem and decomposable distribution. Kybernetika 27(5):403–412.Google Scholar
  • Jorion P (2001) Value at Risk: The New Benchmark for Managing Financial Risk (McGraw-Hill, New York).Google Scholar
  • Kellerer HG (1964) Verteilungsfunktionen mit gegebenen marginalverteilungen. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3(4): 247–270.CrossrefGoogle Scholar
  • Kellerer HG (1991) Indecomposable marginal problems. Dall’aglio G, Kotz SI, Salinetti G, eds. Advances in Probability Distributions with Given Marginals, Mathematics and Its Applications, Vol. 67 (Kluwer Academic Publisher, Dordrecht, the Netherlands), 139–149.CrossrefGoogle Scholar
  • Kendall MG (1938) A new measure of rank correlation. Biometrika 30(1–2):81–93.CrossrefGoogle Scholar
  • Kleinberg J, Rabani Y, Tardos E (2000) Allocating bandwidth for bursty connections. SIAM J. Comput. 30(1):191–217.CrossrefGoogle Scholar
  • Kreinovich V, Ferson S (2006) Computing best-possible bounds for the distribution of a sum of several variables is NP-hard. Internat. J. Approximate Reasoning 41(3):331–342.CrossrefGoogle Scholar
  • Lasserre JB (2006) Convergent sdp-relaxations in polynomial optimization with sparsity. SIAM J. Optim. 17(3):833–843.CrossrefGoogle Scholar
  • Lauritzen SL, Speed TP, Vijayan K (1984) Decomposable graphs and hypergraphs. J. Australian Math. Soc. 36(1):12–29.CrossrefGoogle Scholar
  • Lim AEB, Shanthikumar JG, Vahn G-Y (2011) Conditional value-at-risk in portfolio optimization: Coherent but fragile. Oper. Res. Lett. 39(3):163–171.CrossrefGoogle Scholar
  • Makarov GD (1982) Estimates for the distribution function of the sum of two random variables with given marginal distributions. Theory Probab. Its Appl. 26(4):803–806.CrossrefGoogle Scholar
  • Markowitz HM (1952) Portfolio selection. J. Finance 7(1):77–91.Google Scholar
  • Meilijson I, Nadas A (1979) Convex majorization with an application to the length of critical path. J. Appl. Probab. 16(3):671–677.CrossrefGoogle Scholar
  • Merton RC (1980) On estimating the expected return on the market: An exploratory investigation. J. Financial Econom. 8(4):323–361.CrossrefGoogle Scholar
  • Natanzon A, Shamir R, Sharan R (2000) A polynomial approximation algorithm for the minimum fill-in problem. SIAM J. Comput. 30(4):1067–1079.CrossrefGoogle Scholar
  • Natarajan K, Sim M, Uichanco J (2009a) Tractable robust expected utility and risk models for portfolio optimization. Oper. Res. 20(4):695–731.Google Scholar
  • Natarajan K, Song M, Teo CP (2009b) Peristency model and its applications in choice modeling. Management Sci. 55(3):453–469.LinkGoogle Scholar
  • Nemirovski A, Shapiro A (2006) Convex approximations of chance constrained programs. SIAM J. Optim. 17(4):969–996.CrossrefGoogle Scholar
  • Puccetti G, Rüschendorf L (2012) Bounds for joint portfolios of dependent risks. Statist. Risk Model. 29(2):107–132.CrossrefGoogle Scholar
  • Pucetti G, Rüschendorf L (2013) Sharp bounds for sums of dependent risks. J. Appl. Probab. 50(1):42–53.CrossrefGoogle Scholar
  • Rachev ST, Rüschendorf L (1989) Mass Transportation Problems, Vol. I–II (Springer, Berlin).Google Scholar
  • Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J. Risk 2(3):21–41.CrossrefGoogle Scholar
  • Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J. Banking Finance 26(7):1443–1471.CrossrefGoogle Scholar
  • Rose DJ, Tarjan RE, Lueker GS (2004) Algorithmic aspects of vertex elimination on graphs. SIAM J. Comput. 5(2):266–283.CrossrefGoogle Scholar
  • Rüschendorf L (1982) Random variables with maximum sums. Adv. Appl. Probab. 14(3):695–731.CrossrefGoogle Scholar
  • Rüschendorf L (1991) Bounds for distributions with multivariate marginals. Mosler K, Scarsini M, eds. Stochastic Orders and Decision under Risk, IMS Lecture Notes—Monograph Series 19 (Institute of Mathematical Statistics, Beachwood, OH), 285–310.CrossrefGoogle Scholar
  • Rüschendorf L (2005) Stochastic ordering of risks, influence of dependence and a.s. constructions. Balakrishnan N, Bairamov IG, Gebizlioglu OL, eds. Advances on Models, Characterizations and Applications (CRC Press, Boca Raton), 19–56.CrossrefGoogle Scholar
  • Tarjan RE, Yannakakis M (1984) Simple linear-time algorithms to test chordality of graph, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J. Comput. 13(3):566–579.CrossrefGoogle Scholar
  • Vorob’ev NN (1962) Consistent families of measures and their extensions. Theory Probab. Its Appl. 7(2):147–163.CrossrefGoogle Scholar
  • Wainwright MJ, Jordan MI (2008) Graphical models, exponential families, and variational inference. Foundations Trends Machine Learn. 1(1–2):1–305.Google Scholar
  • Wang B, Wang R (2011) The complete mixability and convex minimization problems with monotone marginal densities. J. Multivariate Anal. 102(10):1344–1360.CrossrefGoogle Scholar
  • Wang H, Song M (2011) Ckmeans.1d.dp: Optimal k-means clustering in one dimension by dynamic programming. The R Journal 3(2):29–33.CrossrefGoogle Scholar
  • Yannakakis M (1981) Computing the minimum fill-in is NP-complete. SIAM J. Algebraic and Discrete Methods 2(1):77–79.CrossrefGoogle Scholar
  • Zhu S, Fukushima M (2009) Worst-case conditional value-at-risk with application to robust portfolio management. Oper. Res. 57(5): 1155–1168.LinkGoogle Scholar
  • Zymler S, Kuhn D, Rustem B (2013) Worst-case value at risk of nonlinear portfolios. Management Sci. 59:172–188.LinkGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.