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

UR - http://www.scopus.com/inward/citedby.url?scp=79956318822&partnerID=8YFLogxK

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 -