Laura Angeloni

Existence of financial equilibria in a multi-period stochastic economy

We consider the model of a stochastic financial exchange economy with finitely many periods. Time and uncertainty are represented by a finite event-tree \( \mathbb{D} \) and consumers may have constraints on their portfolios. We provide a general existence result of financial equilibria, which allows to cover several important cases of financial structures in the literature with or without constraints on portfolios.

Approximation with Respect to Goffman–Serrin Variation by Means of Non-Convolution Type Integral Operators

We obtain strong convergence results and order of approximation for a class of linear non-convolution type integral operators in the space , where denotes the space of all the L 1-functions with bounded ℱ-variation in endowed with the norm Here, ℱ is a positive sublinear functional defined on ℝ N and μ f is the derivative (vector) measure associated to f. Some meaningful examples are discussed.

Approximation Results with Respect to Multidimensional φ-Variation for Nonlinear Integral Operators

In this paper we study approximation problems for functions belonging to BV φ-spaces (spaces of functions of bounded φ-variation) in multidimensional setting. In particular, using a multidimensional concept of φ-variation in the sense of Tonelli introduced in [4], we obtain estimates, convergence results and, by means of suitable Lipschitz classes, results about the order of approximation for a family of nonlinear convolution integral operators.

A Characterization of Absolute Continuity by means of Mellin Integral Operators

In the case of classical convolution operators, an important characterization of absolute continuity is given in terms of convergence in variation. In this paper we will study this problem for Mellin integral operators, proving analogous characterizations in the frame of the classical BV -spaces, both in the one-dimensional and in the multidimensional setting.

Convergence in variation and a characterization of the absolute continuity

We study approximation results for a family of Mellin integral operators of the form where is a family of kernels, , , and f is a function of bounded variation on . The starting point of this study is motivated by the important applications that approximation properties of certain families of integral operators have in image reconstruction and in other fields. In order to treat such problems, to work in BV -spaces in the multidimensional setting of becomes crucial: for this reason we use a multidimensional concept of variation in the sense of Tonelli, adapted from the classical definition to the present setting of equipped with the Haar measure. Using such definition of variation, we obtain a convergence result proving that , as , whenever f is an absolutely continuous function; moreover we also study the problem of the rate of approximation. In case of regular kernels, we finally prove a characterization of the absolute continuity in terms of the convergence in variation by means of the Mellin-type operators .

Convergence and rate of approximation in

In this paper we study convergence results and rate of approximation for a family of linear integral operators of Mellin type in the frame of

BV^{\varphi}(\mathbb R^N_+)

BV^{\varphi}(\mathbb{R}^N_+)

for a class of Mellin integral operators

. Here

Variation and Approximation in Multidimensional Setting for Mellin Integral Operators

BV^{\varphi}(\mathbb{R}^N_+)

A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded Variation

denotes the space of functions with bounded