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.

(2016). Asymptotic stochastic dominance rules for sums of i.i.d. random variables [journal article - articolo]. In JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. Retrieved from http://hdl.handle.net/10446/52752

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

ORTOBELLI LOZZA, Sergio;LANDO, Tommaso;PETRONIO, Filomena;
2016-01-01

Abstract

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.
articolo
2016
ORTOBELLI LOZZA, Sergio; Lando, Tommaso; Petronio, Filomena; Tichy, Tomas
(2016). Asymptotic stochastic dominance rules for sums of i.i.d. random variables [journal article - articolo]. In JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. Retrieved from http://hdl.handle.net/10446/52752
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