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Portfolio selection through and extremality stochastic order

  • Romo, Juan
  • Pellerey, Franco
  • Lillo, Rosa E.
  • Laniado, Henry
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    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.

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    Paper provided by Universidad Carlos III de Madrid. Departamento de Estadística in its series DES - Working Papers. Statistics and Econometrics. WS with number ws121812.

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    Date of creation: Jun 2012
    Date of revision:
    Handle: RePEc:cte:wsrepe:ws121812
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    1. Marco Scarsini & Yosef Rinott, 2006. "Total positivity order and the normal distribution," Post-Print hal-00538990, HAL.
    2. Hadar, Josef & Russell, William R., 1971. "Stochastic dominance and diversification," Journal of Economic Theory, Elsevier, vol. 3(3), pages 288-305, September.
    3. 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.
    4. 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.
    5. Franco Pellerey & Patrizia Semeraro, 2005. "A Note on the Portfolio Selection Problem," Theory and Decision, Springer, vol. 59(4), pages 295-306, December.
    6. Landsman, Zinoviy & Tsanakas, Andreas, 2006. "Stochastic ordering of bivariate elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 488-494, March.
    7. 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.
    8. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    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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