Multivariate measures of positive dependence

In this paper a set of desirable properties for measures of positive dependence of ordered n-tuples of continuous random variables (n >= 2) is proposed and a class of multivariate positive dependence measures is introduced. We consider the comonotonicity dependence structure as the strong dependency structure and so the class consists of measures that take values in the range [0, 1] and are defined in such a way that they equal 1 in case the random vector is comonotonic and equal 0 in case it is independent.

Preference Rapresentation for Multicriteria Decision Making

In this note we consider a multicriteria decision problem where the decision maker know the the state of the world but the set of consequences is multidimensional. We suppose that a value function is specified over the attribute of the decision problem and we analyze some classes of non additive functions that can represent interaction between criteria.Multicriteria decision making, value functions, Choquet signed integral, Schur decreasing functions. functions

Swim-like motion of bodies immersed in an ideal fluid

The connection between swimming and control theory is attracting increasing attention in the recent literature. Starting from an idea of Alberto Bressan [A. Bressan, Discrete Contin. Dyn. Syst. 20 (2008) 1\u201335]. we study the system of a planar body whose position and shape are described by a finite number of parameters, and is immersed in a 2-dimensional ideal and incompressible fluid in terms of gauge field on the space of shapes. We focus on a class of deformations measure preserving which are diffeomeorphisms whose existence is ensured by the Riemann Mapping Theorem. After making the first order expansion for small deformations, we face a crucial problem: the presence of possible non vanishing initial impulse. If the body starts with zero initial impulse we recover the results present in literature (Marsden, Munnier and oths). If instead the body starts with an initial impulse different from zero, the swimmer can self-propel in almost any direction if it can undergo shape changes without any bound on their velocity. This interesting observation, together with the analysis of the controllability of this system, seems innovative. Mathematics Subject Classification. 74F10, 74L15, 76B99, 76Z10. Received June 14, 2016. Accepted March 18, 2017. 1. Introduction In this work we are interested in studying the self-propulsion of a deformable body in a fluid. This kind of systems is attracting an increasing interest in recent literature. Many authors focus on two different type of fluids. Some of them consider swimming at micro scale in a Stokes fluid [2,4\u20136,27,35,40], because in this regime the inertial terms can be neglected and the hydrodynamic equations are linear. Others are interested in bodies immersed in an ideal incompressible fluid [8,18,23,30,33] and also in this case the hydrodynamic equations turn out to be linear. We deal with the last case, in particular we study a deformable body -typically a swimmer or a fish- immersed in an ideal and irrotational fluid. This special case has an interesting geometric nature and there is an attractive mathematical framework for it. We exploit this intrinsically geometrical structure of the problem inspired by [32,39,40], in which they interpret the system in terms of gauge field on the space of shapes. The choice of taking into account the inertia can apparently lead to a more complex system, but neglecting the viscosity the hydrodynamic equations are still linear, and this fact makes the system more manageable. The same fluid regime and existence of solutions of these hydrodynamic equations has been studied in [18] regarding the motion of rigid bodies

Aggregation functions: an approach using copulae

In this paper we present the extension of the copula approach to aggregation functions. In fact we want to focus on a class of aggregation functions and present them in the multilinear form with marginal copulae. Moreover, we define the joint aggregation density function.

Multivariate dependence modeling using copulas

There exist necessary and sufficient conditions on the generating functions of the FGM family, in order to obtain various dependence properties. We present multivariate generalizations of this class studying symmetry and dependence concepts, measuring the dependence among the components of each class and providing several examples.copula, density function, FGM copulas, dependence, symmetry

On the characterization of convex premium principles

In actuarial literature the properties of risk measures or insurance premium principles have been extensively studied . We propose a characterization of a particular class of coherent risk measures defined in [1]. The considered premium principles are obtained by expansion of TVar measures, consequently they look like very interesting in insurance pricing where TVar measures is frequently used to value tail risks.risk measures, premium principles, capacity, distortion function, TVar

On non-monotonic Choquet integrals as aggregation functions

This paper deals with non-monotonic Choquet integral, a generalization of the regular Choquet integral. The discrete non-monotonic Choquet integral is considered under the viewpoint of aggregation. In particular we give an axiomatic characterization of the class of non-monotonic Choquet integrals.We show how the Shapley index, in contrast with the monotonic case, can assume positive values if the criterion is in average a benefit, depending on its effect in all the possible coalition coalitions, and negative values in the opposite case of a cost criterion.

A copula-based approach to aggregation functions

This paper presents the role of copula functions in the theory of aggregation operators and an axiomatic characterization of Archimedean aggregation functions. In this context we are focusing our attention about several properties of aggregation functions, like supermodularity and Schur-concavity.Aggregation functions, supermodularity, Schur-concavity, copula, Archimedean copulae

On characterization of a class of convex operators for pricing insurance risks

The properties of risk measures or insurance premium principles have been extensively studied in actuarial literature. We propose an axiomatic description of a particular class of coherent risk measures defined in Artzner, Delbaen, Eber, and Heath (1999). The considered risk measures are obtained by expansion of TVar measures, consequently they look like very interesting in insurance pricing where TVar measures is frequently used to value tail risks.Risk measures, premium principles,Choquet measures distortion function,TVar .

An Ordinal Approach to Risk Measurement

In this short note, we aim at a qualitative framework for modeling multivariate risk. To this extent, we consider completely distributive lattices as underlying universes, and make use of lattice functions to formalize the notion of risk measure. Several properties of risk measures are translated into this general setting, and used to provide axiomatic characterizations. Moreover, a notion of quantile of a lattice-valued random variable is proposed, which shown to retain several desirable properties of its real-valued counterpart.lattice; risk measure; Sugeno integral; quantile.