Weighted Quasi-arithmetic Means and Conditional Expectations

In this paper, the weighted quasi-arithmetic means are discussed from the viewpoint of utility functions and background risks in economics, and they are represented by weighting functions and conditional expectations. Using these representations, an index for background risks in stochastic environme...

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Bibliographic Details
Published inModeling Decisions for Artificial Intelligence Vol. 6408; pp. 31 - 42
Main Author Yoshida, Yuji
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Conditional Expectation
Risk Averse
Risk Premium
Utility Function
Weighting Function
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Summary:In this paper, the weighted quasi-arithmetic means are discussed from the viewpoint of utility functions and background risks in economics, and they are represented by weighting functions and conditional expectations. Using these representations, an index for background risks in stochastic environments is derived through the weighted quasi-arithmetic means. The first-order stochastic dominance and the risk premium are demonstrated using the weighted quasi-arithmetic means and the aggregated mean ratios, and they are characterized by the background risk index. Finally, examples of the weighted quasi-arithmetic mean and the aggregated mean ratio for various typical utility functions are given.
ISBN:3642162916
9783642162916
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-16292-3_6