Changes in multiplicative background risk and risk-taking behavior

This article analyzes the conditions under which any change in a multiplicative background risk induces a more cautious behavior. We give necessary and sufficient conditions under which any change in the multiplicative background risk with respect to the Nth-degree stochastic dominance raises local risk aversion. Surprisingly, decreasing relative risk aversion of any order up to N in the sense of Pratt (Econometrica 32:122–136, <CitationRef CitationID="CR10">1964</CitationRef>) coupled with decreasing relative risk aversion in the sense of Ross (Econometrica 49:631–638, <CitationRef CitationID="CR13">1981</CitationRef>) are sufficient to guarantee an increase in local risk aversion after any deterioration of the multiplicative background risk thanks to the Nth-degree stochastic dominance. We link our results concerning second-order stochastic dominance with the concept of multiplicative risk vulnerability. Copyright Springer Science+Business Media New York 2013