This paper characterizes aversion to one risk in the presence of another, which is invulnerable to the size of exposure to the former risk and consistent with the common bivariate risk preferences for combining good with bad. We show that all bivariate utility functions that satisfy bivariate risk apportionment exhibit risk aversion with two risks if, and only if, the dependence structure of the two risks is characterized by the notion of expectation dependence. We then propose an intensity measure of risk aversion with two risks that is based on the utility premium normalized by the marginal utility evaluated at an arbitrarily chosen pair. We show that the intensity measure being uniformly larger is equivalent to the concept of greater generalized Ross risk aversion. An application for optimal prevention in a two-period model is presented when the dependence structure of the underlying random variables is governed by the notion of expectation dependence.

本文描述了在存在另一种风险的情况下对一种风险的厌恶，这种厌恶不受前一种风险的影响规模的影响，并且与将好坏结合的常见双变量风险偏好一致。我们表明，当且仅当两种风险的依赖结构具有期望依赖的概念时，所有满足双变量风险分配的双变量效用函数都表现出具有两种风险的风险厌恶。然后，我们提出了一种具有两种风险的风险规避强度度量，该度量基于效用溢价，由在任意选择的对中评估的边际效用归一化。我们表明，强度度量一致地更大相当于更大的广义罗斯风险厌恶的概念。