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(U,V) ordering and a duality theorem for risk aversion and Lorenz type orderings

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  • Giovagnoli, Alessandra
  • Wynn, Henry P.

Abstract

There is a duality theory connecting certain stochastic orderings between cumulative distribution functions F1 , F2 and stochastic orderings between their inverses F −1 , F −1. This underlies some theories of utility in the case of the cdf and deprivation indices in the case of the inverse. Under certain conditions there is an equivalence between the two theories. An example is the equivalence between second order stochastic dominance and the Lorenz ordering. This duality is generalised to include the case where there is “distortion” of the cdf of the form v(F ) and also of the inverse. A comprehensive duality theorem is presented in a form which includes the distortions and links the duality to the parallel theories of risk and deprivation indices. It is shown that some well-known examples are special cases of the results, including some from the Yaari social welfare theory and the theory of majorization.

Suggested Citation

  • Giovagnoli, Alessandra & Wynn, Henry P., 2012. "(U,V) ordering and a duality theorem for risk aversion and Lorenz type orderings," LSE Research Online Documents on Economics 55856, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:55856
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    File URL: http://eprints.lse.ac.uk/55856/
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    Cited by:

    1. Marco Capaldo & Antonio Di Crescenzo & Alessandra Meoli, 2024. "Cumulative information generating function and generalized Gini functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(7), pages 775-803, October.

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    More about this item

    Keywords

    income inequality; prospect theory; stochastic orderings; utility theory; Yaari’s functionals;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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