Conditional implicit mean and the law of iterated integrals

研究成果: Article査読

2 被引用数 (Scopus)

抄録

This paper presents a new framework which generalizes the concept of conditional expectation to mean values which are implicitly defined as unique solutions to some functional equation. We call such a mean value an implicit mean. The implicit mean and its very special example, the quasi-linear mean, have been extensively applied to economics and decision theory. This paper provides a procedure of defining the conditional implicit mean and then analyzes its properties. In particular, we show that the conditional implicit mean is in general "biased" in the sense that an analogue of the law of iterated expectations does not hold and we characterize the quasi-linear mean as the only implicit mean which is "unbiased".

本文言語English
ページ(範囲)1-15
ページ数15
ジャーナルJournal of Mathematical Economics
45
1-2
DOI
出版ステータスPublished - 2009 1 20

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics

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