Heavy tails for an alternative stochastic perpetuity model
Heavy tails for an alternative stochastic perpetuity model
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DOI：
10.1016/j.spa.2018.12.008
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发表时间：
2019-11-01
影响因子：
1.4
通讯作者：
Wintenberger, Olivier
中科院分区：
文献类型：
--
作者：
Mikosch, Thomas;Rezapour, Mohsen;Wintenberger, Olivier
在本文中，我们考虑了一个永久型随机模型。与Kesten(1973)和Goldie(1991)的经典仿射永续模型不同，该模型中的所有贴现因子都是相互独立的。我们证明了该模型的分布的尾部在单变量和多变量情况下都是规则变化的。由于模型中的额外随机性，尾部不像Kesten-Goldie设置那样是纯粹的幂定律，而是涉及对数项。(C)2018爱思唯尔B.V.保留所有权利。
In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten (1973) and Goldie (1991) all discount factors in the model are mutually independent. We prove that the tails of the distribution of this model are regularly varying both in the univariate and multivariate cases. Due to the additional randomness in the model the tails are not pure power laws as in the Kesten-Goldie setting but involve a logarithmic term. (C) 2018 Elsevier B.V. All rights reserved.