We consider a variant of the caching problem, where each request is a set of pages of a fixed size, instead of a single page. In order to serve such a request, we require at least one of those pages to be present in the cache. Each page is assumed to have unit size and unit cost for getting loaded into the cache. We prove lower bounds on the competitive ratio for this problem in both the determ...

In this paper we propose a downside risk measure, the expectile-based Value at Risk (EVaR), which is more sensitive to the magnitude of extreme losses than the conventional quantile-based VaR (QVaR). The index θ of an EVaR is the relative cost of the expected margin shortfall and hence reflects the level of prudentiality. It is also shown that a given expectile corresponds to the quantiles with...

Let S be a finite set. Let k be a positive integer. Let A be a subset of Sk satisfying |A| = |S|k−1. Let B = Sk \ A. For every v ∈ Sk and every i ∈ {1, 2, . . . , k}, we denote by vi the i-th component of the k-tuple v (remember that v is an element of Sk, that is, a k-tuple of elements of S). Then, every v ∈ Sk satisfies v = (v1, v2, . . . , vk). Let F be the set of all pairs (a, b) ∈ A × B fo...