Asymptotic stochastic dominance rules for sums of i.i.d. random variables

作者：Ortobelli Sergio^*; Lando Tommaso; Petronio Filomena; Tichy Tomas

来源：Journal of Computational and Applied Mathematics, 2016, 300: 432-448.

DOI：10.1016/j.cam.2015.12.017

• Asymmetry
• Heavy tails
• Stable Paretian distribution
• Stochastic dominance

In this paper, we deal with stochastic dominance rules under the assumption that the random variables are stable distributed. The stable Paretian distribution is generally used to model a wide range of phenomena. In particular, its use in several applicative areas is mainly justified by the generalized central limit theorem, which states that the sum of a number of i.i.d. random variables with heavy tailed distributions tends to a stable Paretian distribution. We show that the asymptotic behavior of the tails is fundamental for establishing a dominance in the stable Paretian case. Moreover, we introduce a new weak stochastic order of dispersion, aimed at evaluating whether a random variable is more "risky" than another under condition of maximum uncertainty, and a stochastic order of asymmetry, aimed at evaluating whether a random variable is more or less asymmetric than another. The theoretical results are confirmed by a financial application of the obtained dominance rules. The empirical analysis shows that the weak order of risk introduced in this paper is generally a good indicator for the second order stochastic dominance.

• 出版日期2016-7