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Inverse stochastic dominance constraints and rank dependent expected utility theory

  • Darinka Dentcheva

    (Stevens Institute of Technology)

  • Andrzej Ruszczynski

    (Rutgers University)

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.

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Paper provided by EconWPA in its series GE, Growth, Math methods with number 0503001.

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Length: 17 pages
Date of creation: 11 Mar 2005
Date of revision:
Handle: RePEc:wpa:wuwpge:0503001
Note: Type of Document - pdf; pages: 17
Contact details of provider: Web page: http://econwpa.repec.org

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  1. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  2. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  4. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Portfolio Optimization With Stochastic Dominance Constraints," Finance 0402016, EconWPA, revised 02 Mar 2006.
  5. repec:dgr:rugsom:02a33 is not listed on IDEAS
  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. 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.
  9. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-39, November.
  10. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
  11. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
  12. 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.
  13. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  14. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Optimization Under First Order Stochastic Dominance Constraints," GE, Growth, Math methods 0403002, EconWPA, revised 07 Aug 2005.
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