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...</citationref></citationref>

We study Aumann and Serrano's (2008) risk index for sums of gambles that are not necessarily independent. We show that if the dependent parts of two gambles are similarly ordered, or more generally positively quadrant dependent, then the risk index of the sum of two gambles is always larger than...