The Experts below are selected from a list of 60 Experts worldwide ranked by ideXlab platform

Gianluca Cassese - One of the best experts on this subject based on the ideXlab platform.

  • the theorem of halmos and savage under Finite Additivity
    Journal of Mathematical Analysis and Applications, 2016
    Co-Authors: Gianluca Cassese
    Abstract:

    Abstract We prove an extension to the Finitely additive setting of the theorem of Halmos and Savage. From this we deduce extensions of classical results of Drewnowski and of Yan as well as a new characterization of weak compactness in the space of Finitely additive set functions.

  • Convergence in measure under Finite Additivity
    Sankhya A, 2013
    Co-Authors: Gianluca Cassese
    Abstract:

    We investigate the possibility of replacing the topology of convergence in probability with convergence in L ^1, upon a change of the underlying measure under Finite Additivity. We establish conditions for the continuity of linear operators and convergence of measurable sequences, including a Finitely additive analog of Komlós Lemma. We also prove several topological implications. Eventually, a characterization of continuous linear functionals on the space of measurable functions is obtained.

  • convergence in measure under Finite Additivity
    arXiv: Functional Analysis, 2013
    Co-Authors: Gianluca Cassese
    Abstract:

    We investigate the possibility of replacing the topology of convergence in probability with convergence in L 1 , upon a change of the underlying measure under nite Additivity. We es- tablish conditions for the continuity of linear operators and convergence of measurable sequences, including a nitely additive analogue of Koml os Lemma. We also prove several topological impli- cations. Eventually, a characterization of continuous linear functionals on the space of measurable functions is obtained.

Enrique Miranda - One of the best experts on this subject based on the ideXlab platform.

  • SMPS - The F. Riesz Representation Theorem and Finite Additivity
    Soft Methods for Handling Variability and Imprecision, 2020
    Co-Authors: Gert De Cooman, Enrique Miranda
    Abstract:

    A positive and normalised real linear functional on the set of bounded continuous functions can be characterised as the integral of a σ-additive probability measure, by the F. Riesz Representation Theorem. In this paper, we look at the Finitely additive extensions of such a functional to the set of all bounded random variables, and prove that they are determined by Riesz’ extension to lower semi-continuous functions. In doing so, we establish links with Daniell’s approach to integration, Walley’s theory of coherent lower previsions, and de Finetti’s Representation Theorem for exchangeable random variables.

  • the f riesz representation theorem and Finite Additivity
    Soft Methods in Probability and Statistics, 2008
    Co-Authors: Gert De Cooman, Enrique Miranda
    Abstract:

    A positive and normalised real linear functional on the set of bounded continuous functions can be characterised as the integral of a σ-additive probability measure, by the F. Riesz Representation Theorem. In this paper, we look at the Finitely additive extensions of such a functional to the set of all bounded random variables, and prove that they are determined by Riesz’ extension to lower semi-continuous functions. In doing so, we establish links with Daniell’s approach to integration, Walley’s theory of coherent lower previsions, and de Finetti’s Representation Theorem for exchangeable random variables.

  • The Hausdorff Moment Problem under Finite Additivity
    Journal of Theoretical Probability, 2007
    Co-Authors: Enrique Miranda, Gert De Cooman, Erik Quaeghebeur
    Abstract:

    We investigate to what extent Finitely additive probability measures on the unit interval are determined by their moment sequence. We do this by studying the lower envelope of all Finitely additive probability measures with a given moment sequence. Our investigation leads to several elegant expressions for this lower envelope, and it allows us to conclude that the information provided by the moments is equivalent to the one given by the associated lower and upper distribution functions.

Gert De Cooman - One of the best experts on this subject based on the ideXlab platform.

  • SMPS - The F. Riesz Representation Theorem and Finite Additivity
    Soft Methods for Handling Variability and Imprecision, 2020
    Co-Authors: Gert De Cooman, Enrique Miranda
    Abstract:

    A positive and normalised real linear functional on the set of bounded continuous functions can be characterised as the integral of a σ-additive probability measure, by the F. Riesz Representation Theorem. In this paper, we look at the Finitely additive extensions of such a functional to the set of all bounded random variables, and prove that they are determined by Riesz’ extension to lower semi-continuous functions. In doing so, we establish links with Daniell’s approach to integration, Walley’s theory of coherent lower previsions, and de Finetti’s Representation Theorem for exchangeable random variables.

  • the f riesz representation theorem and Finite Additivity
    Soft Methods in Probability and Statistics, 2008
    Co-Authors: Gert De Cooman, Enrique Miranda
    Abstract:

    A positive and normalised real linear functional on the set of bounded continuous functions can be characterised as the integral of a σ-additive probability measure, by the F. Riesz Representation Theorem. In this paper, we look at the Finitely additive extensions of such a functional to the set of all bounded random variables, and prove that they are determined by Riesz’ extension to lower semi-continuous functions. In doing so, we establish links with Daniell’s approach to integration, Walley’s theory of coherent lower previsions, and de Finetti’s Representation Theorem for exchangeable random variables.

  • The Hausdorff Moment Problem under Finite Additivity
    Journal of Theoretical Probability, 2007
    Co-Authors: Enrique Miranda, Gert De Cooman, Erik Quaeghebeur
    Abstract:

    We investigate to what extent Finitely additive probability measures on the unit interval are determined by their moment sequence. We do this by studying the lower envelope of all Finitely additive probability measures with a given moment sequence. Our investigation leads to several elegant expressions for this lower envelope, and it allows us to conclude that the information provided by the moments is equivalent to the one given by the associated lower and upper distribution functions.

Alexander R. Pruss - One of the best experts on this subject based on the ideXlab platform.

  • Avoiding Dutch Books despite inconsistent credences
    Synthese, 2020
    Co-Authors: Alexander R. Pruss
    Abstract:

    It is often loosely said that Ramsey (in: Braithwaite (ed) The foundations of mathematics and other logical essays, Routledge and Kegan Paul, Abingdon, pp 156–198, 1931) and de Finetti (in: Kyburg, Smokler (eds) Studies in subjective probability, Kreiger Publishing, Huntington, 1937) proved that if your credences are inconsistent, then you will be willing to accept a Dutch Book, a wager portfolio that is sure to result in a loss. Of course, their theorems are true, but the claim about acceptance of Dutch Books assumes a particular method of calculating expected utilities given the inconsistent credences. I will argue that there are better ways of calculating expected utilities given a potentially inconsistent credence assignment, and that for a large class of credences—a class that includes many inconsistent examples—these ways are immune to Dutch Books and single-shot domination failures. The crucial move is to replace Finite Additivity with Monotonicity (if $$A\subseteq B$$ A ⊆ B , then $$P(A)\le P(B)$$ P ( A ) ≤ P ( B ) ) and then calculate expected utilities for positive U via the formula $$\int _0^\infty P(U>y)\, dy$$ ∫ 0 ∞ P ( U > y ) d y . This shows that Dutch Book arguments for probabilism, the thesis that one’s credences should be consistent, do not establish their conclusion. Finally, I will consider a modified argument based on multi-step domination failure that does better, but nonetheless is not as compelling as the Dutch Book arguments appeared to be.

Peter P. Wakker - One of the best experts on this subject based on the ideXlab platform.

  • Prospect theory for continuous distributions: A preference foundation
    Journal of Risk and Uncertainty, 2011
    Co-Authors: Amit Kothiyal, Vitalie Spinu, Peter P. Wakker
    Abstract:

    Preference foundations give necessary and sufficient conditions for a decision model, stated directly in terms of the empirical primitive: the preference relation. For the most popular descriptive model for decision making under risk and uncertainty today, prospect theory, preference foundations have as yet been provided only for prospects taking Finitely many values. In applications, however, prospects often are complex and involve inFinitely many values, as in normal and lognormal distributions. This paper provides a preference foundation of prospect theory for such complex prospects. We allow for unbounded utility and only require Finite Additivity of the underlying probability distributions, leaving the restriction to countably additive distributions optional. As corollaries, we generalize previously obtained preference foundations for special cases of prospect theory (rank-dependent utility and Choquet expected utility) that all required countable Additivity. We now obtain genuine generalizations of de Finetti’s and Savage’s Finitely additive setups to unbounded utility.