Asymptotic stochastic dominance rules for sums of i.i.d. random variables
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摘要
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.
论文关键词:60E15,60E07,91GXX,91G10,Asymmetry,Heavy tails,Stable Paretian distribution,Stochastic dominance
论文评审过程:Received 19 May 2015, Revised 5 October 2015, Available online 22 January 2016, Version of Record 8 February 2016.
论文官网地址:https://doi.org/10.1016/j.cam.2015.12.017