Abstract
This paper extends the work on location-scale (LS) family with general n random seed sources. First, we clarify and generalize existing results in this multivariate setting. Some useful geometrical and topological properties of the location-scale expected utility functions are obtained. Second, we introduce and study some general non-expected utility functions defined over the LS family. Special care is taken in characterizing the shapes of the indifference curves induced by the location-scale expected utility functions and non-expected utility functions. Finally, efforts are also made to study several well-defined partial orders and dominance relations defined over the LS family. These include the first- and second-order stochastic dominances, the mean-variance rule, and a newly defined location-scale dominance.
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This research was initiated during Ma’s visit to National University of Singapore in Spring 2004. The authors are grateful to Professor Charalambos D. Aliprantis and anonymous referees for their substantive comments that have significantly improved this manuscript. We have benefited from useful discussions and correspondence with Professor Thomas Kwok Keung Au, who also drew our attention to the inverse problem associated with the LS expected utility class. We would also like to thank Professor Qingfu Zhang for his comments.
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Wong, WK., Ma, C. Preferences over location-scale family. Econ Theory 37, 119–146 (2008). https://doi.org/10.1007/s00199-007-0254-3
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DOI: https://doi.org/10.1007/s00199-007-0254-3
Keywords
- Location-scale family
- Inverse problem
- Non-expected utility function
- Stochastic dominance
- Location-scale dominance
- Mean-variance rule