Some new classes of consistent risk measures

Some New Classes of Consistent Risk Measures

Many types of insurance premium principles and/or risk measures can be characterized by means of a set of axioms, which in many cases are rather arbitrarily chosen and not always in accordance with economic reality. In the present paper we generalize Yaari’s risk measure by relaxing his axioms. In addition, we derive translation invariant minimal Orlicz risk measures, which we call Haezendonck ...

Time Consistent Dynamic Risk Measures

Some new maximum VC classes

Set systems of finite VC dimension are frequently used in applications relating to machine learning theory and statistics. Two simple types of VC classes which have been widely studied are the maximum classes (those which are extremal with respect to Sauer’s lemma) and so-called Dudley classes, which arise as sets of positivity for linearly parameterized functions. These two types of VC class w...

SSD Consistent Criteria and Coherent Risk Measures

The mean-risk approach quantifies the problem of choice among uncertain prospects in a lucid form of only two criteria: the mean, representing the expected outcome, and the risk: a scalar measure of the variability of outcomes. The model is appealing to decision makers but it may lead to inferior conclusions. Several risk measures, however, can be combined with the mean itself into the robust o...

Some new classes of finite parallelisms

Some new constructions of parallelisms in PG(3, q) are given that produce parallelisms consisting of one Desarguesian spread and q + q derived Knuth semifield spreads and other types consisting of one Knuth semifield spread, one Hall spread and the remaining spreads are derived Knuth semifield spreads.