TY - JOUR
T1 - Risk aversion for variational and multiple-prior preferences
AU - Werner, Jan
PY - 2011/5/1
Y1 - 2011/5/1
N2 - The objective of this paper is to identify variational preferences and multiple-prior (maxmin) expected utility functions that exhibit aversion to risk under some probability measure from among the priors. Risk aversion has profound implications on agents' choices and on market prices and allocations. Our approach to risk aversion relies on the theory of mean-independent risk of Werner (2009). We identify necessary and sufficient conditions for risk aversion of convex variational preferences and concave multiple-prior expected utilities. The conditions are stability of the cost function and of the set of probability priors, respectively, with respect to a probability measure. The two stability properties are new concepts. We show that cost functions defined by the relative entropy distance or other divergence distances have that property. Set of priors defined as cores of convex distortions of probability measures or neighborhoods in divergence distances have that property, too.
AB - The objective of this paper is to identify variational preferences and multiple-prior (maxmin) expected utility functions that exhibit aversion to risk under some probability measure from among the priors. Risk aversion has profound implications on agents' choices and on market prices and allocations. Our approach to risk aversion relies on the theory of mean-independent risk of Werner (2009). We identify necessary and sufficient conditions for risk aversion of convex variational preferences and concave multiple-prior expected utilities. The conditions are stability of the cost function and of the set of probability priors, respectively, with respect to a probability measure. The two stability properties are new concepts. We show that cost functions defined by the relative entropy distance or other divergence distances have that property. Set of priors defined as cores of convex distortions of probability measures or neighborhoods in divergence distances have that property, too.
KW - Mean-independent risk
KW - Multiple-prior expected utility
KW - Risk aversion
KW - Variational preferences
UR - http://www.scopus.com/inward/record.url?scp=79956318822&partnerID=8YFLogxK
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U2 - 10.1016/j.jmateco.2010.08.020
DO - 10.1016/j.jmateco.2010.08.020
M3 - Article
AN - SCOPUS:79956318822
VL - 47
SP - 382
EP - 390
JO - Journal of Mathematical Economics
JF - Journal of Mathematical Economics
SN - 0304-4068
IS - 3
ER -