Weighted quasi-arithmetic means and conditional expectations

Authors:
Yuji Yoshida
Affiliations:
Faculty of Economics and Business Administration, University of Kitakyushu, Kitakyushu, Japan
Venue:
MDAI'10 Proceedings of the 7th international conference on Modeling decisions for artificial intelligence
Year:
2010

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Abstract

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.