Randomly weighted sums of subexponential random variables with application to capital allocation
Randomly weighted sums of subexponential random variables with application to capital allocation
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DOI：
10.1007/s10687-014-0191-z
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发表时间：
2014-05
期刊：
影响因子：
1.3
通讯作者：
Q. Tang;Zhongyi Yuan
中科院分区：
文献类型：
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作者：
Q. Tang;Zhongyi Yuan
我们感兴趣的是随机加权和的尾部行为，其中主要随机变量X1，…，Xn是实值的、独立的和次指数分布的，而随机权重𝜃1、…，𝜃N是非负的和任意依赖的，但独立于X1，…、Xn.对于各种重要情况，我们证明了的尾概率渐近等价于𝜃1X1，…的尾概率之和，𝜃nXn，符合单次大跳跃原则。最后给出了该模型在资本配置中的应用。
We are interested in the tail behavior of the randomly weighted sum, in which the primary random variablesX1, …,Xnare real valued, independent and subexponentially distributed, while the random weights𝜃1, …,𝜃nare nonnegative and arbitrarily dependent, but independent ofX1, …,Xn. For various important cases, we prove that the tail probability ofis asymptotically equivalent to the sum of the tail probabilities of𝜃1X1, …,𝜃nXn, which complies with the principle of a single big jump. An application to capital allocation is proposed.