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, 1964) coupled with decreasing relative risk aversion in the sense of Ross (Econometrica 49:631–638, 1981) 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.