A unifying view on some problems in probability and statistics

被引:4
|
作者
Berti, Patrizia [1 ]
Pratelli, Luca [2 ]
Rigo, Pietro [3 ]
机构
[1] Univ Modena & Reggio Emilia, Dipartimento Matemat Pura & Applicata G Vitali, I-41100 Modena, Italy
[2] Acad Navale, I-57100 Livorno, Italy
[3] Univ Pavia, Dipartimento Matemat F Casorati, I-27100 Pavia, Italy
来源
STATISTICAL METHODS AND APPLICATIONS | 2014年 / 23卷 / 04期
关键词
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; EXISTENCE; THEOREM;
D O I
10.1007/s10260-014-0272-9
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Let L be a linear space of real random variables on the measurable space (Omega, A). Conditions for the existence of a probability P on A such that E-P vertical bar X vertical bar < infinity and E-P(X) = 0 for all X is an element of L are provided. Such a P may be finitely additive or sigma-additive, depending on the problem at hand, and may also be requested to satisfy P similar to P-0 or P << P-0 where 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 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.
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页码:483 / 500
页数:18
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