We start by pointing out a simple property of risk apportionment with additive risks in the general stochastic dominance context defined by Eeckhoudt et al. (2009b). Quite generally, an observed preference for risk apportionment with additive risks in a specific risk environment is preserved when the decision-maker is confronted to other risk situations, so long as the total order of stochastic dominance relationships among pairs of risks remains the same. Our objective is to check whether this simple property also holds for multiplicative risk environments. We show that this is not the case, in general, but that the property holds and more strongly for the case of CRRA utility functions. This is due to a particular feature of CRRA functions that we unveil.

中文翻译：

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加法和乘法风险分配的新结果

我们首先指出在 Eeckhoudt 等人定义的一般随机优势上下文中具有附加风险的风险分配的简单属性。(2009b)。一般而言，当决策者面临其他风险情况时，只要风险对之间的随机支配关系的总顺序保持不变，就会保留在特定风险环境中对具有附加风险的风险分配的观察偏好。我们的目标是检查这个简单的属性是否也适用于乘法风险环境。我们表明，一般情况下并非如此，但是对于 CRRA 效用函数的情况，该性质成立并且更加强烈。这是由于我们推出的 CRRA 功能的一个特殊功能。