On Aumann and Serrano’s economic index of risk

We study the risk index of an additive gamble proposed in Aumann and Serrano (J Political Econ 116(5):810–836, <CitationRef CitationID="CR2">2008</CitationRef>). We establish a generalized duality result for this index and use it to prove Yaari (J Econ Theory 1:315–329, <CitationRef CitationID="CR19">1969</CitationRef>) alternative characterization of DARA utilities. A new characterization result for the risk index is obtained through essentially monotonic risk aversion utilities. We also extend the domain of gambles by introducing a price for gambles. We then develop a theory on the risk index for multiplicative gambles. Relative risk aversion functions for multiplicative gambles play the same role as absolute risk aversion functions for additive gambles. Copyright Springer-Verlag Berlin Heidelberg 2014