Abstract
Stochastic approximation of a given time series {∑j=1kXjYj} by a linear combination of simpler sequences {∑j=1kXj} and {∑j=1kYj} is treated uniformly over k∈{1,…,n}. A maximal inequality is proven in order to find a sharp bound on Value-at-Risk of max1≤k≤n|∑j=1kXjYj|.
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