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Inverse stochastic dominance constraints and rank dependent expected utility theory

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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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ, 07030, USA

    Darinka Dentcheva

  2. Department of Management Science and Information Systems, Rutgers University, Piscataway, NJ, 08854, USA

    Andrzej Ruszczyński

Authors
  1. Darinka Dentcheva
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  2. Andrzej Ruszczyński
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Corresponding author

Correspondence to Andrzej Ruszczyński.

Additional information

Research supported by the NSF awards DMS-0303545, DMS-0303728, DMI-0354500 and DMI-0354678.

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Dentcheva, D., Ruszczyński, A. Inverse stochastic dominance constraints and rank dependent expected utility theory. Math. Program. 108, 297–311 (2006). https://doi.org/10.1007/s10107-006-0712-x

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  • DOI: https://doi.org/10.1007/s10107-006-0712-x

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