Josep E. Peris

A new characterization of inverse-positive matrices

Abstract The author provides a new characterization of inverse-positive matrices using positive splittings. It is shown that a matrix M is inverse-positive iff the spectral radius of all positive splittings is less than one. Then a single positive splitting is found, called a B -splitting, such that M is inverse-positive iff it allows for a B -splitting satisfying the spectral radius bound.

A weak utility function for acyclic preferences

Abstract The purpose of this paper is to provide a continuous weak utility function for acyclic preferences which characterizes the maximal elements of the binary relation in terms of the maxima of this function.

Maximal elements of not necessarily acyclic binary relations

Abstract The existence of maximal elements for binary relations is analyzed without imposing transitivity or convexity conditions. An acyclic relation is constructed in such a way that some maximal elements of this new relation characterize maximal elements of the original one.

Numerical representation for lower quasi-continuous preferences

A weaker than usual continuity condition for acyclic preferences is introduced. For preorders this condition turns out to be equivalent to lower continuity, but in general this is not true. By using this condition, a numerical representation which is upper semicontinuous is obtained. This fact guarantees the existence of maxima of such a function, and therefore the existence of maximal elements of the binary relation.

A note on adjusting correlation matrices

A new algorithm for adjusting correlation matrices and for comparison with Fingers algorithm, which is used to compute Value-at-Risk in RiskMetrics for stress test scenarios. The solution proposed by the new methodology is always better than Fingers approach in the sense that it alters as little as possible those correlations that one would wish not to alter, but they change in order to obtain a consistent Finger correlation matrix.

A characterization of weak-monotone matrices

Abstract We provide some characterizations of weak-monotone matrices by using positive splittings. We prove that a matrix allowing a generalized B -splitting is weak-monotone iff the associated spectral radius is less than one. Next, we prove that weak- monotone matrices allow a generalized B -splitting. Weak-monotonicity is associated with strong positive solvability of a linear system Ax = b , b ⩾ 0.

A proportional approach to claims problems with a guaranteed minimum

In distribution problems, and specifically in bankruptcy issues, the Proportional (P) and the Egalitarian (EA) divisions are two of the most popular ways to resolve the conflict. Nonetheless, when using the egalitarian division, agents may receive more than her claim. We propose a compromise between the proportional and the egalitarian approaches by considering the restriction that no one receives more than her claim. We show that the most egalitarian compromise fulfilling this restriction ensures a minimum amount to each agent. We also show that this compromise can be interpreted as a process that works in two steps as follows: first, all agents receive an equal share up to the smallest claim if possible (egalitarian distribution), and then, the remaining estate (if any) is allocated proportionally to the remaining claims (proportional distribution). Finally, we obtain that the recursive application of this process finishes at the Constrained Equal Awards solution (CEA).

Linear joint-production models

SummaryThe purpose of this paper is to analyze the solvability of linear joint production models (that is the existence of nonnegative solutions for all admissible values of the relevant parameters). A characterization result is provided.

CHOICE FUNCTIONS: RATIONALITY RE-EXAMINED

On analyzing the problem that arises whenever the set of maximal elements is large, and a selection is then required (see Peris & Subiza 1998), we realize that logical ways of selecting among maximals violate the classical notion and axioms of rationality. We arrive at the same conclusion if we analyze solutions to the problem of choosing from a tournament (where maximal elements do not necessarily exist). So, in our opinion the notion of rationality must be discussed, not only in the traditional sense of external conditions (Sen 1993), but in terms of the internal information provided by the binary relation.

A reformulation of von Neumann–Morgenstern stability: m-stability

The notion of a stable set (introduced by von Neumann and Morgenstern, 1944) is an important tool in the field of Decision Theory. However, stable sets may fail to exist. Other stability notions have been introduced in the literature in order to solve the non-existence problem. We propose a new notion, that we call m-stability, and compare it with previous proposals. Moreover, we analyze some properties (existence, uniqueness, unions and intersections, …) of the different notions of a stable set. Finally, we use the Shapley–Scarf market model with indivisible goods in order to show that the non-empty core is an m-stable set, and does not fulfill, in general, the other stability notions.