The problem of the fair allocation of indivisible items is a relevant and challenging economic problem with several applications. For small dimensional frameworks, the problem can be solved exactly by full enumeration of all the possible allocations of the items. For higher dimensional...

For the classic problem of fair allocation of indivisible goods, we introduce the notion of minimum social inequality allocations and discuss its connection to other fair allocation rules such as minimum envy. We show that a fair allocation problem can always be cast as the problem of finding an...

Unlike classic risk sharing problems based on expected utilities or convex risk measures, quantile-based risk sharing games exhibit two special features. First, quantile-based risk measures (such as the Value-at-Risk) are often not convex, and second, they ignore some part of the distribution of...

Two natural and potentially desirable properties for capital allocation rules are top-downconsistency and shrinking independence. Top-down consistency means that the total capital isdetermined by the aggregate portfolio risk. Shrinking independence means that the risk capitalallocated to a given...

In various fields of applications such as capital allocation, sensitivity analysis and systemic risk evaluation, one often needs to compute or estimate the expectation of a random variable given that another random variable is equal to its quantile at some pre-specified probability level. A...