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Price uniqueness and fundamental theorem of asset pricing with finitely additive probabilities
Stochastics, 2013 Let L be a linear space of real-bounded random variables on the probability space . A finitely additive probability P on such thatis called equivalent martingale finitely additive probability (EMFA). In this paper, EMFAs are investigated in case P0 is atomic. Existence of EMFAs is characterized and a question raised in Berti et al. (2012, J.
Patrizia Berti +2 more
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Pragmatic entropy for finitely additive probabilities
, 1983 The definition of entropy is extended to finitely additive probability distributions on a countable set, making use of coding theorems. This entropy is set equal to \(+\infty\), since non-countably additive sources are never compressible through block-coding.
Andrea Sgarro
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Sufficient Conditions for the Existence of a Finitely Additive Probability Measure [PDF]
The Annals of Mathematical Statistics, 1967 R. Duncan Luce
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A general principle for limit theorems in finitely additive probability: The dependent case
Journal of Multivariate Analysis, 1988 In Trans. Am. Math. Soc. 273, 541-550 (1982; Zbl 0507.60012), the author has proved a general principle, i.e. almost all limit theorems that are true in countably additive probability theory are also true in finitely additive probability theory in the independent case. Here, this result is generalized to the dependent case on the same line.
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On the semimetric on a Boolean algebra induced by a finitely additive probability measure [PDF]
Pacific Journal of Mathematics, 1982 Thomas E. Armstrong, Karel Prikry
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Remarks on continuously distributed sequences
Karpatsʹkì Matematičnì Publìkacìï, 2021 In the first part of the paper we define the notion of the density as certain type of finitely additive probability measure and the distribution function of sequences with respect to the density.
M. Paštéka
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Solving a Paradox of Evidential Equivalence [PDF]
, 2021 David Builes presents a paradox concerning how confident you should be that any given member of an infinite collection of fair coins landed heads, conditional on the information that they were all flipped and only finitely many of them landed heads.
Dorr, Cian +2 more
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The Kullback–Leibler Information Function for Infinite Measures
Entropy, 2016 In this paper, we introduce the Kullback–Leibler information function ρ ( ν , μ ) and prove the local large deviation principle for σ-finite measures μ and finitely additive probability measures ν.
Victor Bakhtin, Edvard Sokal
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The Hausdorff moment problem under finite additivity [PDF]
, 2007 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.
De Cooman, Gert +2 more
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The Foundations of Probability with Black Swans
Journal of Probability and Statistics, 2010 We extend the foundation of probability in samples with rare events that are potentially catastrophic, called black swans, such as natural hazards, market crashes, catastrophic climate change, and species extinction. Such events are generally treated as ‘
Graciela Chichilnisky
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