Two random variables are called comonotone when there is an increasing relation between them, in the sense that when one of them increases (decreases), the other one also increases (decreases). This notion has been widely investigated in probability theory, and is related to the theory of copulas. This contribution studies the notion of comonotonicity in an imprecise setting. We define comonoto...

We give a complete characterization of both comonotone and not comonotone coherent risk measures in the discrete finite probability space, where each outcome is equally likely. To the best of our knowledge, this is the first work that characterizes and distinguishes comonotone and not comonotone coherent risk measures via AVaR representation in the discrete finite probability space of equally l...

This paper focuses on the study of decision making under risk. We, first, recall some model-free definitions of risk aversion and increase in risk. We propose a new form of behavior under risk that we call anti-monotone risk aversion (hereafter referred to as ARA) related to the concept of anti-comonotony a concept investigated in Abouda, Aouani and Chateauneuf (2008). Note that many research h...

This paper focuses on the study of decision making under risk. We, first, recall some model-free definitions of risk aversion and increase in risk. We propose a new form of behavior under risk that we call anti-monotone risk aversion (hereafter referred to as ARA) related to the concept of anti-comonotony a concept investigated in Abouda, Aouani and Chateauneuf (2008). Note that many research h...

Axiomatic generalizations of OWA operators are introduces and discussed. First, OMA operators based on comonotone modularity are recalled. Then, several kinds of comonotone pseudoadditivity based OWA generalizations are characterized and exemplified. Some of already known OWA generalizations are thus seen from new points of view. In several cases an integral representation of generalized OWA op...

An approach to the Shannon and Rényi entropy maximization problems with constraints on the mean and law invariant deviation measure for a random variable has been developed. The approach is based on the representation of law invariant deviation measures through corresponding convex compact sets of nonnegative concave functions. A solution to the problem has been shown to have an alpha-concave d...

Let f be a continuous function on ?1; 1], which changes its monotonicity nitely many times in the interval, say s times. In the rst part of this paper we have discussed the validity of Jackson type estimates for the approximation of f by algebraic polynomials that are comonotone with it. We have proved the validity of a Jackson type estimate involving the Ditzian {Totik ((rst) modulus of contin...