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Two stochastic dominance criteria based on tail comparisons

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Listed:
  • Julio Mulero
  • Miguel A. Sordo
  • Marilia C. de Souza
  • Alfonso Suárez‐LLorens

Abstract

Actuarial risks and financial asset returns are typically heavy tailed. In this paper, we introduce 2 stochastic dominance criteria, called the right‐tail order and the left‐tail order, to compare these variables stochastically. The criteria are based on comparisons of expected utilities, for 2 classes of utility functions that give more weight to the right or the left tail (depending on the context) of the distributions. We study their properties, applications, and connections with other classical criteria, including the increasing convex and the second‐order stochastic dominance. Finally, we rank some parametric families of distributions and provide empirical evidence of the new stochastic dominance criteria with an example using real data.

Suggested Citation

  • Julio Mulero & Miguel A. Sordo & Marilia C. de Souza & Alfonso Suárez‐LLorens, 2017. "Two stochastic dominance criteria based on tail comparisons," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(6), pages 575-589, November.
    • Handle: RePEc:wly:apsmbi:v:33:y:2017:i:6:p:575-589
    DOI: 10.1002/asmb.2260
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    References listed on IDEAS

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    1. Chen, Zhiping & Yang, Li, 2011. "Nonlinearly weighted convex risk measure and its application," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1777-1793, July.
    2. Wei, Wang & Yatracos, Yannis, 2004. "A stop-loss risk index," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 241-250, April.
    3. Bauwens, Luc & Laurent, Sebastien, 2005. "A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 346-354, July.
    4. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    5. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    6. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    7. Barry Arnold & Robert Beaver & A. Azzalini & N. Balakrishnan & A. Bhaumik & D. Dey & C. Cuadras & J. Sarabia & Barry Arnold & Robert Beaver, 2002. "Skewed multivariate models related to hidden truncation and/or selective reporting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 7-54, June.
    8. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    9. Adelchi Azzalini & Giuliana Regoli, 2012. "Some properties of skew-symmetric distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 857-879, August.
    10. Tsanakas, Andreas & Barnett, Christopher, 2003. "Risk capital allocation and cooperative pricing of insurance liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 239-254, October.
    11. Matthias Scherer & Svetlozar T. Rachev & Young Shin Kim & Frank J. Fabozzi, 2012. "Approximation of skewed and leptokurtic return distributions," Applied Financial Economics, Taylor & Francis Journals, vol. 22(16), pages 1305-1316, August.
    12. Kevin Fergusson & Eckhard Platen, 2006. "On the Distributional Characterization of Daily Log-Returns of a World Stock Index," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 19-38.
    13. Alexander Cherny & Dilip Madan, 2009. "New Measures for Performance Evaluation," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2371-2406, July.
    14. Edward Furman & Ričardas Zitikis, 2009. "Weighted Pricing Functionals With Applications to Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(4), pages 483-496.
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    Cited by:

    1. Belzunce, Félix & Martínez-Riquelme, Carolina, 2023. "A new stochastic dominance criterion for dependent random variables with applications," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 165-176.

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