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Portfolio Optimization With Stochastic Dominance Constraints

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  • Darinka Dentcheva

    (Stevens Institute of Technology)

  • Andrzej Ruszczynski

    (Rutgers University)

Abstract

We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints on the portfolio return. We develop optimality and duality theory for these models. We construct equivalent optimization models with utility functions. Numerical illustration is provided.

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File URL: http://128.118.178.162/eps/fin/papers/0402/0402016.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0402016.

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Date of creation: 19 Feb 2004
Date of revision: 02 Mar 2006
Handle: RePEc:wpa:wuwpfi:0402016

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Web page: http://128.118.178.162

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Keywords: portfolio optimization; stochastic dominance; risk; utility functions; duality;

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References

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  1. W. Ogryczak & A. Ruszczynski, 1997. "From Stochastic Dominance to Mean-Risk Models: Semideviations as Risk Measures," Working Papers ir97027, International Institute for Applied Systems Analysis.
  2. Andrzej Ruszczynski & Robert J. Vanderbei, 2003. "Frontiers of Stochastically Nondominated Portfolios," Econometrica, Econometric Society, vol. 71(4), pages 1287-1297, 07.
  3. Hanoch, G & Levy, Haim, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 335-46, July.
  4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  5. Sharpe, William F., 1971. "A Linear Programming Approximation for the General Portfolio Analysis Problem," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(05), pages 1263-1275, December.
  6. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  7. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
  8. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
  9. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Convexification of Stochastic Ordering," GE, Growth, Math methods 0402005, EconWPA, revised 05 Aug 2005.
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Citations

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Cited by:
  1. Roman, Diana & Mitra, Gautam & Zverovich, Victor, 2013. "Enhanced indexation based on second-order stochastic dominance," European Journal of Operational Research, Elsevier, vol. 228(1), pages 273-281.
  2. Laetitia Andrieu & Michel De Lara & Babacar Seck, 2009. "Conditional Value-at-Risk Constraint and Loss Aversion Utility Functions," Papers 0906.3425, arXiv.org.
  3. Haim Shalit & Shlomo Yitzhaki, 2008. "How Does Beta Explain Stochastic Dominance Efficiency?," Working Papers 0813, Ben-Gurion University of the Negev, Department of Economics.
  4. Behr, Patrick & Guettler, Andre & Truebenbach, Fabian, 2012. "Using industry momentum to improve portfolio performance," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1414-1423.
  5. Laetitia Andrieu & Michel De Lara & Babacar Seck, 2008. "Conditional Value-at-Risk Constraint and Loss Aversion Utility Functions," Working Papers hal-00390836, HAL.
  6. Darinka Dentcheva & Andrzej Ruszczynski, 2005. "Inverse stochastic dominance constraints and rank dependent expected utility theory," GE, Growth, Math methods 0503001, EconWPA.
  7. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2011. "Optimizing international portfolios with options and forwards," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3188-3201.
  8. Andrey Lizyayev, 2010. "Stochastic Dominance Efficiency Analysis of Diversified Portfolios: Classification, Comparison and Refinements," Tinbergen Institute Discussion Papers 10-084/2, Tinbergen Institute.
  9. Babacar Seck & Laetitia Andrieu & Michel De Lara, 2012. "Parametric multi-attribute utility functions for optimal profit under risk constraints," Theory and Decision, Springer, vol. 72(2), pages 257-271, February.
  10. Alessandra Cillo & Philippe Delquié, 2013. "Mean-Risk Analysis with Enhanced Behavioral Content," Working Papers 498, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  11. Andrey M. Lizyayev, 2009. "Stochastic Dominance: Convexity and Some Efficiency Tests," Tinbergen Institute Discussion Papers 09-112/2, Tinbergen Institute, revised 05 Jan 2010.
  12. Lizyayev, Andrey & Ruszczyński, Andrzej, 2012. "Tractable Almost Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 218(2), pages 448-455.
  13. Anissa Chaibi & Maria-Lenuta Ciupac-Ulici & Mircea-Cristian Gherman, 2014. "Do Recent Stochastic Tools Help to Better Understand Investors’ Preference and Asset Allocation?," Working Papers 2014-130, Department of Research, Ipag Business School.
  14. Liesiö, Juuso & Salo, Ahti, 2012. "Scenario-based portfolio selection of investment projects with incomplete probability and utility information," European Journal of Operational Research, Elsevier, vol. 217(1), pages 162-172.

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