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Inverse stochastic dominance constraints and rank dependent expected utility theory

Author

Listed:
  • Darinka Dentcheva

    (Stevens Institute of Technology)

  • Andrzej Ruszczynski

    (Rutgers University)

Abstract

We consider optimization problems with second order stochastic dominance constraints formulated as a relation of Lorenz curves. We characterize the relation in terms of rank dependent utility functions, which generalize Yaari's utility functions. We develop optimality conditions and duality theory for problems with Lorenz dominance constraints. We prove that Lagrange multipliers associated with these constraints can be identified with rank dependent utility functions. The problem is numerically tractable in the case of discrete distributions with equally probable realizations.

Suggested Citation

  • Darinka Dentcheva & Andrzej Ruszczynski, 2005. "Inverse stochastic dominance constraints and rank dependent expected utility theory," GE, Growth, Math methods 0503001, EconWPA.
  • Handle: RePEc:wpa:wuwpge:0503001
    Note: Type of Document - pdf; pages: 17
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/ge/papers/0503/0503001.pdf
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    References listed on IDEAS

    as
    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. repec:dgr:rugsom:02a33 is not listed on IDEAS
    3. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
    4. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    5. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    6. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
    7. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Convexification of Stochastic Ordering," GE, Growth, Math methods 0402005, EconWPA, revised 05 Aug 2005.
    8. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    9. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Optimization Under First Order Stochastic Dominance Constraints," GE, Growth, Math methods 0403002, EconWPA, revised 07 Aug 2005.
    10. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    11. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    12. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    13. Darinka Dentcheva & Andrzej Ruszczynski, 2005. "Inverse stochastic dominance constraints and rank dependent expected utility theory," GE, Growth, Math methods 0503001, EconWPA.
    14. Klein Haneveld, Willem K. & Vlerk, Maarten H. van der, 2002. "Integrated chance constraints: reduced forms and an algorithm," Research Report 02A33, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    15. Muliere, Pietro & Scarsini, Marco, 1989. "A note on stochastic dominance and inequality measures," Journal of Economic Theory, Elsevier, vol. 49(2), pages 314-323, December.
    16. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    Citations

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    Cited by:

    1. Dentcheva Darinka & Stock Gregory J. & Rekeda Ludmyla, 2011. "Mean-risk tests of stochastic dominance," Statistics & Risk Modeling, De Gruyter, vol. 28(2), pages 97-118, May.
    2. Dentcheva, Darinka & Penev, Spiridon, 2010. "Shape-restricted inference for Lorenz curves using duality theory," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 403-412, March.
    3. Lizyayev, Andrey & Ruszczyński, Andrzej, 2012. "Tractable Almost Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 218(2), pages 448-455.
    4. Neslihan Fidan Keçeci & Viktor Kuzmenko & Stan Uryasev, 2016. "Portfolios Dominating Indices: Optimization with Second-Order Stochastic Dominance Constraints vs. Minimum and Mean Variance Portfolios," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 9(4), pages 1-14, October.
    5. Andrey Lizyayev, 2010. "Stochastic Dominance Efficiency Analysis of Diversified Portfolios: Classification, Comparison and Refinements," Tinbergen Institute Discussion Papers 10-084/2, Tinbergen Institute.
    6. Darinka Dentcheva & Andrzej Ruszczynski, 2005. "Inverse stochastic dominance constraints and rank dependent expected utility theory," GE, Growth, Math methods 0503001, EconWPA.

    More about this item

    Keywords

    Stochastic Dominance; Lorenz Curve; Yaari's Dual Utility; Rank Dependent Expected Utility; Optimality; Duality;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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