TY - JOUR

T1 - Conditional implicit mean and the law of iterated integrals

AU - Ozaki, Hiroyuki

PY - 2009/1/20

Y1 - 2009/1/20

N2 - 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".

AB - 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".

KW - Conditioning

KW - Implicit mean

KW - Law of iterated integrals

UR - http://www.scopus.com/inward/record.url?scp=57649105539&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57649105539&partnerID=8YFLogxK

U2 - 10.1016/j.jmateco.2008.06.001

DO - 10.1016/j.jmateco.2008.06.001

M3 - Article

AN - SCOPUS:57649105539

VL - 45

SP - 1

EP - 15

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

IS - 1-2

ER -