A unifying view on some problems in probability and statistics

Patrizia Berti, Luca Pratelli and Pietro Rigo ()

Statistical Methods & Applications, 2014, vol. 23, issue 4, 483-500

Abstract: Let $$L$$ L be a linear space of real random variables on the measurable space $$(\varOmega ,\mathcal {A})$$ ( Ω , A ) . Conditions for the existence of a probability $$P$$ P on $$\mathcal {A}$$ A such that $$E_P|X|>\infty $$ E P | X | > ∞ and $$E_P(X)=0$$ E P ( X ) = 0 for all $$X\in L$$ X ∈ L are provided. Such a $$P$$ P may be finitely additive or $$\sigma $$ σ -additive, depending on the problem at hand, and may also be requested to satisfy $$P\sim P_0$$ P ∼ P 0 or $$P\ll P_0$$ P ≪ P 0 where $$P_0$$ P 0 is a reference measure. As a motivation, we note that a plenty of significant issues reduce to the existence of a probability $$P$$ P as above. Among them, we mention de Finetti’s coherence principle, equivalent martingale measures, equivalent measures with given marginals, stationary and reversible Markov chains, and compatibility of conditional distributions. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Compatibility of conditional distributions; De Finetti’s coherence principle; Equivalent martingale measure; Equivalent probability measure with given marginals; Finitely additive probability; Fundamental theorem of asset pricing (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10260-014-0272-9

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