5,140 research outputs found
Generic Existence and Robust Non Existence of Numeraires in Finite Dimensional Securities Markets
No full textWe supply necessary and sufficient conditions for the existence of numeraires. We also supply a characterization of robust non-existence of numeraires
Existence of invariant masses. An elementary treatment.
No full textWe prove by means of very elementary tools the existence of a finitely additive probability invariant under the elements of a commuting family of transformations
On the axiomatic treatment of the Φ-mean
No full textWe extends to masses on a real interval the notion of Φ-mean, usually considered in the context of σ-additive probabilities or probability distribution functions, and consider some axiomatic treatments of it at different levels of masses (simple masses, compact support masses. tight masses, arbitrary masses). Moreover, as an important special case, we get axiomatic systems for general means, as well. We also prove that the usual axiomatic system "Consistency with Certainty + Associativity + Monotonicity" characterizes the Φ-mean of masses with arbitrary compact support and that, already at tight masses level, this system is not adequate. We note that the analytical tool used to define the Φ-mean is the Choquet integral
Weak convergence of masses on normal topological spaces
No full textThe purpose of the paper is to continue and reinterpret de Finetti's work on adherent probabilities in the context of masses on topological spaces. In this way we obtain some basic results regarding the weak convergence of masses on normal topological spaces
A characterization of neo-additive measures
No full textNeo-additive and generalized neo-additive capacities were introduced in order to capture both optimistic and pessimistic attitudes towards uncertainty without abandoning the subjective probabilistic approach. In this way, one can obtain, as particular cases, some well-known decision criteria (via Choquet expectation) adopted in Decision Theory and Mathematical Statistics.
In order to introduce these capacities, Chateauneuf, Eichberger, Grant and Eichberger, Grant, Lefort consider three types of events: universal, null and essential events; afterwardsthey introduce capacities which are null on null events (null property), assume value one on universal events (normalization property) and are translations of finitely additive probabilities on the family of essential events. Finally, they supply a theoretic measure characterization of these type of capacities.
In this paper, we introduce neo-additive measures as monotone measures which are translations of finitely additive ones on the family of essential events, without assumption of normalization property and null property. Moreover, we supply a simple and natural theoretic characterization of these measures obtaining, as particular cases, the corresponding results of the previous authors. In this way, our results give a robust foundation of neo-additive and generalized neo-additive capacities in abstract measure setting
Weak convergence of masses: some neighborhood systems
No full textMany fundamental theorems in the classical countably additive probability theory are related with the notion of weak convergence of measures as, for instance, asymptotic results, Prokhorov theorems and metrizability conditions for the space of probability measures. In order to extend these results in a finitely additive setting, in this paper we introduce some different neighborhood systems for the topology of the weak convergence of masses
Regular and purely irregular bounded charges: a decomposition theorem
No full textWe introduce the notion of regular and purely irregular charges with respect to a pair of pavings and study their structural properties. Moreover, we link regularity and σ-additivity, obtaining some generalizations of well-known theorems. Finally, when the pavings satisfy some reasonable weak conditions, we can decompose any bounded charge into regular and purely irregular decomposants; this decomposition becomes the Hewitt-Yosida one, whenever the charges are defined on the Baire σ-field of a countably compact space
A Chebyshev type inequality for Sugeno integral and comonotonicity
No full textWe supply a characterization of comonotonicity property by a Chebyshev type inequality for Sugeno integra
Chebyshev type inequality for Choquet integral and comonotonicity
No full textWe suppply a Chebyshev type inequality for Choquet integral and link this inequality with comonotonicit
The topology of convergence in distribution of masses on the real line
No full textWe introduce the topology of convergence in distribution of masses on the real line and state its pseudometrizability, by introducing two equivalent pseudometrics (suitable modifications of the Lévy metric and Kingman-Taylor metric, both considered, in the Literature, in the context of σ-additive probability distribution functions). Moreover, we prove that any bounded set of masses is relatively compact w.r.t. this topology. Finally, we show that the corresponding topological space is a locally compact Polish space
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