IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v53y2013i1p230-236.html
   My bibliography  Save this article

A note on the family of extremality stochastic orders

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668713000656
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2013.04.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Lillo Rodríguez, Rosa Elvira & Pellerey, Franco & Romo, Juan & 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. Marco Scarsini & Alfred Muller, 2001. "Stochastic comparison of random vectors with a common copula," Post-Print hal-00540198, HAL.
    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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Boonen, Tim J. & Liu, Fangda, 2022. "Insurance with heterogeneous preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    2. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    3. Donald C., Rudow, 2005. "Preferences and Increased Risk Aversion under a General Framework of Stochastic Dominance," MPRA Paper 41191, University Library of Munich, Germany, revised 07 Jun 2005.
    4. Marcello Basili & Paulo Casaca & Alain Chateauneuf & Maurizio Franzini, 2017. "Multidimensional Pigou–Dalton transfers and social evaluation functions," Theory and Decision, Springer, vol. 83(4), pages 573-590, December.
    5. Ansari, Jonathan & Rüschendorf, Ludger, 2021. "Ordering results for elliptical distributions with applications to risk bounds," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    6. Fernández-Ponce, J.M. & Pellerey, F. & Rodríguez-Griñolo, M.R., 2011. "A characterization of the multivariate excess wealth ordering," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 410-417.
    7. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    8. Castaño-Martínez, A. & Pigueiras, G. & Sordo, M.A., 2019. "On a family of risk measures based on largest claims," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 92-97.
    9. Chenguang (Allen) Wu & Achal Bassamboo & Ohad Perry, 2019. "Service System with Dependent Service and Patience Times," Management Science, INFORMS, vol. 65(3), pages 1151-1172, March.
    10. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    11. Ra'ul Torres & Rosa E. Lillo & Henry Laniado, 2015. "A Directional Multivariate Value at Risk," Papers 1502.00908, arXiv.org.
    12. Xu Guo & Andreas Wagener & Wing-Keung Wong & Lixing Zhu, 2018. "The two-moment decision model with additive risks," Risk Management, Palgrave Macmillan, vol. 20(1), pages 77-94, February.
    13. Belzunce, Félix & Ruiz, José M. & Suárez-Llorens, Alfonso, 2008. "On multivariate dispersion orderings based on the standard construction," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 271-281, February.
    14. Sordo, Miguel A., 2016. "A multivariate extension of the increasing convex order to compare risks," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 224-230.
    15. Belzunce, Félix & Suárez-Llorens, Alfonso & Sordo, Miguel A., 2012. "Comparison of increasing directionally convex transformations of random vectors with a common copula," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 385-390.
    16. Guoli Mo & Chunzhi Tan & Weiguo Zhang & Xuezeng Yu, 2023. "Dynamic spatiotemporal correlation coefficient based on adaptive weight," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-43, December.
    17. Szego, Giorgio, 2005. "Measures of risk," European Journal of Operational Research, Elsevier, vol. 163(1), pages 5-19, May.
    18. Bäuerle, Nicole & Glauner, Alexander, 2018. "Optimal risk allocation in reinsurance networks," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 37-47.
    19. Amiri, Mehdi & Izadkhah, Salman & Jamalizadeh, Ahad, 2020. "Linear orderings of the scale mixtures of the multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    20. Nicole Bauerle & Alexander Glauner, 2017. "Optimal Risk Allocation in Reinsurance Networks," Papers 1711.10210, arXiv.org.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:230-236. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.