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Tractable Almost Stochastic Dominance

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Author Info

  • Lizyayev, Andrey
  • Ruszczyński, Andrzej

Abstract

LL-Almost Stochastic Dominance (LL-ASD) is a relaxation of the Stochastic Dominance (SD) concept proposed by Leshno and Levy that explains more of realistic preferences observed in practice than SD alone does. Unfortunately, numerical applications of this concept, such as identifying if a given portfolio is efficient or determining a marketed portfolio that dominates a given benchmark, are computationally prohibitive due to the structure of LL-ASD. We propose a new Almost Stochastic Dominance (ASD) concept that is computationally tractable. For instance, a marketed dominating portfolio can be identified by solving a simple linear programming problem. Moreover, the new concept performs well on all the intuitive examples from the literature, and in some cases leads to more realistic predictions than the earlier concept. We develop some properties of ASD, formulate efficient optimization models, and apply the concept to analyzing investors’ preferences between bonds and stocks for the long run.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 218 (2012)
Issue (Month): 2 ()
Pages: 448-455

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Handle: RePEc:eee:ejores:v:218:y:2012:i:2:p:448-455

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Web page: http://www.elsevier.com/locate/eor

Related research

Keywords: Stochastic Dominance; Portfolio optimization; Risk;

References

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  1. Canner, Niko & Mankiw, N Gregory & Weil, David N, 1997. "An Asset Allocation Puzzle," American Economic Review, American Economic Association, vol. 87(1), pages 181-91, March.
  2. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Portfolio Optimization With Stochastic Dominance Constraints," Finance 0402016, EconWPA, revised 02 Mar 2006.
  3. Darinka Dentcheva & Andrzej Ruszczynski, 2005. "Inverse stochastic dominance constraints and rank dependent expected utility theory," GE, Growth, Math methods 0503001, EconWPA.
  4. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  5. Miller, Naomi & Ruszczynski, Andrzej, 2008. "Risk-adjusted probability measures in portfolio optimization with coherent measures of risk," European Journal of Operational Research, Elsevier, vol. 191(1), pages 193-206, November.
  6. Moshe Leshno & Haim Levy, 2002. "Preferred by "All" and Preferred by "Most" Decision Makers: Almost Stochastic Dominance," Management Science, INFORMS, vol. 48(8), pages 1074-1085, August.
  7. Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
  8. 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.
  9. Levy, Moshe, 2009. "Almost Stochastic Dominance and stocks for the long run," European Journal of Operational Research, Elsevier, vol. 194(1), pages 250-257, April.
  10. Markowitz, Harry M, 1976. "Investment for the Long Run: New Evidence for an Old Rule," Journal of Finance, American Finance Association, vol. 31(5), pages 1273-86, December.
  11. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
  12. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1932, October.
  13. Samuelson, Paul A, 1969. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 239-46, August.
  14. Andrzej Ruszczynski & Robert J. Vanderbei, 2003. "Frontiers of Stochastically Nondominated Portfolios," Econometrica, Econometric Society, vol. 71(4), pages 1287-1297, 07.
  15. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
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Citations

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Cited by:
  1. Dupačová, Jitka & Kopa, Miloš, 2014. "Robustness of optimal portfolios under risk and stochastic dominance constraints," European Journal of Operational Research, Elsevier, vol. 234(2), pages 434-441.
  2. Post, Thierry & Kopa, Miloš, 2013. "General linear formulations of stochastic dominance criteria," European Journal of Operational Research, Elsevier, vol. 230(2), pages 321-332.
  3. Denuit, Michel M. & Huang, Rachel J. & Tzeng, Larry Y. & Wang, Christine W., 2014. "Almost marginal conditional stochastic dominance," Journal of Banking & Finance, Elsevier, vol. 41(C), pages 57-66.

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