Let Δ(1)(Y ) be a set of all 2

Copulas [18] link univariate marginal distribution functions into a joint distribution function of the corresponding random vector. In this paper we will deal with bivariate copulas only. Recall that a function C : [0, 1] → [0, 1] is a (bivariate) copula whenever it is grounded, C(x, y) = 0 whenever 0 ∈ {x, y}, it has neutral element 1, C(x, y) = x∧y, whenever 1 ∈ {x, y} and it is 2-increasing,...

We introduce a simple aggregate claims model, which is able to take into account a continuous range of positive dependence between independence and comonotone dependence. It is based on a multivariate extension of the one-parameter bivariate Fréchet copula, which finds a justification as follows. The chosen model uses only one additional dependence parameter, which is chosen such that it yields...

We show, in the Choquet expected utility model, that preference for diversi cation, that is, convex preferences, is equivalent to a concave utility index and a convex capacity. We then introduce a weaker notion of diversi cation, namely \sure diversication." We show that this implies that the core of the capacity is non-empty. The converse holds under concavity of the utility index. This proper...

We prove the existence of comonotone Pareto optimal allocations when decision makers have probabilistic sophisticated variational preferences and thus representing criteria in the class of law invariant robust utilities. In contrast to previous studies, we show that optimal allocations exist also when decision makers have very different preferences, for example characterized by different domain...

A characterization of t-normed integrals was obtained by Luis M. de Campos, María T. Lamata and Serafín Moral (1991) for finite compacta Radul (2022) the general case. Such establishes a correspondence between space capacities homogeneous respect t-norm monotone normalized functionals preserving maximum operation comonotone functions. In fact, we can consider these theorems as non-additive non-...

Extracting structured subgraphs inside large graphs – often known as the planted subgraph problem – is a fundamental question that arises in a range of application domains. This problem is NP-hard in general, and as a result, significant efforts have been directed towards the development of tractable procedures that succeed on specific families of problem instances. We propose a new computation...

We consider the problem of identifying the worst case dependence structure of a portfolio X1, . . . ,Xn of d-dimensional risks, which yields the largest risk of the joint portfolio. Based on a recent characterization result of law invariant convex risk measures the worst case portfolio structure is identified as a μ-comonotone risk vector for some worst case scenario measure μ. It turns out tha...