Decisions under risk are often multidimensional, where the preferences of the decision maker depend on several attributes. For example, an individual might be concerned about both her level of wealth and the condition of her health. Many times the signs of successive cross derivatives of a...

This paper investigates how welfare losses for facing risks change as a function of the number of risk exposures. To that aim, we define the risk apportionment of order n (RA-n) utility premium as a measure of pain associated with facing the passage from one risk to a riskier one. Changes in...

This paper presents a general result on the random selection of an element from an ordered sequence of risks and uses this result to derive additive and cross risk apportionment. Preferences favoring an improvement of the sampling distribution in univariate or bivariate first-order stochastic...