Abstract
This paper discusses the risk aversion within the framework of the uncertainty theory (Liu in Uncertainty theory: A branch of mathematics for modeling human uncertainty. Springer, Berlin, 2010b), and introduces the notions of uncertain expected utility and uncertain risk premium. In terms of the Arrow–Pratt index, an uncertain version of Pratt’s theorem is proved, which offers an effective way to make comparisons between different individuals’ risk-averse attitudes. We suggest that uncertain risk aversion can be used to measure human’s risk-averse attitudes when uncertainty exists due to lack of the observed data, just as probabilistic risk aversion when sufficient data can be obtained. Uncertain risk aversion provides an alternative method to compare the risk aversions between individuals under uncertain situations.
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Acknowledgments
This work was supported in part by grants from the Innovation Program of Shanghai Municipal Education Commission (No. 13ZS065), the National Social Science Foundation of China (No. 13CGL057), and the National Natural Science Foundation of China (No. 71272177).
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Zhou, J., Liu, Y., Zhang, X. et al. Uncertain risk aversion. J Intell Manuf 28, 615–624 (2017). https://doi.org/10.1007/s10845-014-1013-5
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DOI: https://doi.org/10.1007/s10845-014-1013-5