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Conditional implicit mean and the law of iterated integrals

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  • Ozaki, Hiroyuki

Abstract

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".

Suggested Citation

  • Ozaki, Hiroyuki, 2009. "Conditional implicit mean and the law of iterated integrals," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 1-15, January.
    • Handle: RePEc:eee:mateco:v:45:y:2009:i:1-2:p:1-15
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    References listed on IDEAS

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    6. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
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    Cited by:

    1. Amit Kothiyal & Vitalie Spinu & Peter P. Wakker, 2014. "Average Utility Maximization: A Preference Foundation," Operations Research, INFORMS, vol. 62(1), pages 207-218, February.

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