Aspirational Preferences and Their Representation by Risk Measures (Online Appendix)
David B. Brown
Duke University - Decision Sciences
Enrico G. De Giorgi
University of St. Gallen - SEPS: Economics and Political Sciences
NUS Business School, National University of Singapore
February 2, 2012
This is the appendix to "Aspirational Preferences and Their Representation by Risk Measures," which can be found at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1406399
We consider choice over uncertain, monetary payoffs and study a general class of preferences. These preferences favor diversification, except perhaps on a subset of sufficiently disliked acts, over which concentration is instead preferred. This structure encompasses a number of known models (e.g., expected utility and several variants under a concave utility function). We show that such preferences share a representation in terms of a family of measures of risk and targets. Specifically, the choice function is equivalent to selection of a maximum index level such that the risk of beating the target at that level is acceptable. This representation may help to uncover new models of choice. One that we explore in detail is the special case when the targets are bounded. This case corresponds to a type of satisfying and has descriptive relevance. Moreover, the model is amenable to large-scale optimization.
Number of Pages in PDF File: 7
Keywords: Representation of choice, risk measures, aspiration levels, decision theory paradoxes
JEL Classification: D81working papers series
Date posted: February 15, 2012
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