Catálogo de publicaciones - libros

This paper has two main parts. In the first part, we discuss the existence and uniqueness of the -solution of a second order differential equation with two boundary points conditions in a finite dimensional space, governed by controls which are measures on a compact metric space. We also discuss the dependence on the controls and the variational properties of the value function () := sup(()), associated with a bounded lower semicontinuous function . In the second main part, we discuss the limiting behaviour of a sequence of dynamics governed by second order evolution inclusions with two boundary points conditions. We prove that (up to extracted sequences) the solutions stably converge to a Young measure and we show that the limit measure satisfies a Fatou-type lemma in Mathematical Economics with variational-type inclusion property.

As a generalization of a result by Kusuoka (2001), we provide the representation of law invariant convex risk measures. Very particular cases of law invariant coherent and convex risk measures are also studied.

A method in demand analysis based on the Monge—Kantorovich duality is developed. We characterize (insatiate) demand functions that are rationalized, in different meanings, by concave utility functions with some additional properties such as upper semi-continuity, continuity, non-decrease, strict concavity, positive homogeneity and so on. The characterizations are some kinds of abstract cyclic monotonicity strengthening revealed preference axioms, and also they may be considered as an extension of the Afriat—Varian theory to an arbitrary (infinite) set of ‘observed data’. Particular attention is paid to the case of smooth functions.

This paper investigates the real indeterminacy of equilibria in an incomplete market model in which there are two periods, with uncertainty in the second, and both real and nominal assets exist. As is well known, the equilibria of a model with real assets behave very differently from the equilibria of a model with nominal assets. Then, what happens if real and nominal assets coexist? In this paper it is demonstrated within a general framework that regardless of the presence of real assets there is generically still real indeterminacy of equilibria whose degree is the same as without the real assets.

We present some observations about links between some classical theories of microeconomics and dualities which have been used in optimization theory and in the study of first-order Hamilton-Jacobi equations. We introduce a variant of the classical indirect utility function called the wary indirect utility function and a variant of the expenditure function. We focus the attention on the links between these functions, observing that they have better relationships with the direct functions than their classical forms and we give economic interpretations of them.