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Portfolio selection through and extremality stochastic order

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  • Laniado Rodas, Henry
  • Romo Urroz, Juan
  • Pellerey, Franco
  • Lillo Rodríguez, Rosa Elvira

Abstract

In this paper we introduce a new multivariate stochastic order that compares random vectors in a direction which is determined by a unit vector, generalizing previous upper and lower orthant order. The main properties of this new order, together with its relationships with other multivariate stochastic orders, are investigated and, we present some examples of application in the determination of optimal allocations of wealth among risks in single period portfolio problems.

Suggested Citation

  • Laniado Rodas, Henry & Romo Urroz, Juan & Pellerey, Franco & Lillo Rodríguez, Rosa Elvira, 2012. "Portfolio selection through and extremality stochastic order," DES - Working Papers. Statistics and Econometrics. WS ws121812, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws121812
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    References listed on IDEAS

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    1. Landsman, Zinoviy, 2004. "On the generalization of Esscher and variance premiums modified for the elliptical family of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 563-579, December.
    2. Rinott, Yosef & Scarsini, Marco, 2006. "Total positivity order and the normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1251-1261, May.
    3. Franco Pellerey & Patrizia Semeraro, 2005. "A Note on the Portfolio Selection Problem," Theory and Decision, Springer, vol. 59(4), pages 295-306, December.
    4. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    5. Landsman, Zinoviy & Tsanakas, Andreas, 2006. "Stochastic ordering of bivariate elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 488-494, March.
    6. Hadar, Josef & Russell, William R., 1971. "Stochastic dominance and diversification," Journal of Economic Theory, Elsevier, vol. 3(3), pages 288-305, September.
    7. Bauerle, Nicole & Muller, Alfred, 2006. "Stochastic orders and risk measures: Consistency and bounds," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 132-148, February.
    8. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    9. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    Cited by:

    1. Laniado Rodas, Henry & Lillo Rodríguez, Rosa Elvira & Torres Díaz, Raúl Andrés & Michele, Carlo de, 2016. "Directional multivariate extremes in environmental phenomena," DES - Working Papers. Statistics and Econometrics. WS 23419, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Torres, Raúl & Lillo, Rosa E. & Laniado, Henry, 2015. "A directional multivariate value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 111-123.
    3. Ra'ul Torres & Rosa E. Lillo & Henry Laniado, 2015. "A Directional Multivariate Value at Risk," Papers 1502.00908, arXiv.org.

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