Fear of loss, inframodularity, and transfers

A. Müller, M. SCARSINI

Journal of Economic Theory

July 2012, vol. 147, n°4, pp.1490-1500

Departments: Economics & Decision Sciences

Keywords: Mean preserving spread, Integral stochastic orders, Risk aversion, Ultramodularity, Dual cones

There exist several characterizations of concavity for univariate functions. One of them states that a function is concave if and only if it has nonincreasing differences. This definition provides a natural generalization of concavity for multivariate functions called inframodularity. Inframodular transfers are defined and it is shown that a finite lottery is preferred to another by all expected utility maximizers with an inframodular utility if and only if the first lottery can be obtained from the second via a sequence of inframodular transfers. This result is a natural multivariate generalization of Rothschild and Stiglitz's construction based on mean preserving spreads.