Abstract Stochastic approximation of a given time series { ∑ j = 1 k X j Y j } by a linear combination of simpler sequences { ∑ j = 1 k X j } and { ∑ j = 1 k Y j } is treated uniformly over k ∈ { 1 , … , n } . A maximal inequality is proven in order to find a sharp bound on Value-at-Risk of max 1 ≤ k ≤ n | ∑ j = 1 k X j Y j | .

中文翻译：

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近似因随机变量的乘积之和

摘要 给定时间序列 { ∑ j = 1 k X j Y j } 通过更简单序列 { ∑ j = 1 k X j } 和 { ∑ j = 1 k Y j } 的线性组合的随机逼近在 k 上被统一处理∈ { 1 , … , n } 。证明最大不等式是为了找到最大 1 ≤ k ≤ n | 的风险价值的尖锐界限。∑ j = 1 k X j Y j | .