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A note on the family of extremality stochastic orders

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  • López-Díaz, María Concepción
  • López-Díaz, Miguel

Abstract

The family of extremality stochastic orders was introduced in Laniado et al. (2012) (Portfolio selection through an extremality stochastic order. Insurance: Mathematics and Economics 51, 1–9), as an extension of the upper and lower orthant orders, having important applications in the research of optimal allocations of wealth among risks in single period portfolio problems. In this paper we analyze some properties of such a family of stochastic orders, namely we prove that any extremality stochastic order is generated by a partial order on the Euclidean space and the class of upper quadrant sets of the partial order, showing that all the extremality orders are order-isomorphic. The above analysis will lead to the determination of the maximal generator of each extremality order by means of the maximal generator of the upper orthant order. Moreover we introduce a new family of stochastic orders which arises from the previous construction.

Suggested Citation

  • López-Díaz, María Concepción & López-Díaz, Miguel, 2013. "A note on the family of extremality stochastic orders," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 230-236.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:230-236
    DOI: 10.1016/j.insmatheco.2013.04.009
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    References listed on IDEAS

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    1. Alessandra Giovagnoli & Johnny Marzialetti & Henry Wynn, 2008. "A new approach to inter-rater agreement through stochastic orderings: the discrete case," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 349-370, April.
    2. Pellerey, Franco & Laniado Rodas, Henry, 2012. "Portfolio selection through and extremality stochastic order," DES - Working Papers. Statistics and Econometrics. WS ws121812, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Alfred Müller & Marco Scarsini, 2001. "Stochastic Comparison of Random Vectors with a Common Copula," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 723-740, November.
    4. Laniado, Henry & Lillo, Rosa E. & Pellerey, Franco & Romo, Juan, 2012. "Portfolio selection through an extremality stochastic order," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 1-9.
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    More about this item

    Keywords

    Extremality order; Maximal generator; Order-isomorphism; Order-preserving mapping; Partial order;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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