Generalized multiplicative risk apportionment

This work examines apportionment of multiplicative risks by considering three dominance orderings: first-degree stochastic dominance, Rothschild and Stiglitz's increase in risk and downside risk increase. We use the relative nth-degree risk aversion measure and decreasing relative nth-degree risk aversion to provide conditions guaranteeing the preference for 'harm disaggregation' of multiplicative risks. Further, we relate our conclusions to the preference toward bivariate lotteries, which interpret correlation-aversion, cross-prudence and cross-temperance.