Can a Coherent Risk Measure Be Too Subadditive?

How Superadditive Can a Risk Measure Be?

In this paper, we study the extent to which any risk measure can lead to superadditive risk assessments, implying the potential for penalizing portfolio diversification. For this purpose we introduce the notion of extreme-aggregation risk measures. The extreme-aggregation measure characterizes the most superadditive behavior of a risk measure, by yielding the worst-possible diversification rati...

Testing Can Be Formal, Too

The paper presents a theory of program testing based on formal specifications. The formal semantics of the specifications is the basis for a notion of an exhaustive test set. Under some minimal hypotheses on the program under test, the success of this test set is equivalent to the satisfaction of the specification. The selection of a finite subset of the exhaustive test set can be seen as the i...

Can We Be Too Careful?

When Can a Risk Measure Be Updated Consistently?

In this paper we aim at finding conditions under which risk measures can be consistently updated. Since the class of risk measures that allow dynamically consistent updates appears to be limited, we consider weaker notions of consistency in addition to dynamic consistency, concentrating on notions that are still strong enough to ensure uniqueness of updating. We show that a weak type of consist...

Too Much Information Can Be Too Much for Learning Eciently

In designing learning algorithms it seems quite reasonable to construct them in a way such that all data the algorithm already has obtained are correctly and completely re ected in the description the algorithm outputs on these data. However, this approach may totally fail, i.e., it may lead to the unsolvability of the learning problem, or it may exclude any e cient solution of it. In particula...