We study the problem of a planner who resolves risk–return trade-offs – like financial investment decisions – on behalf of a collective of agents with heterogeneous risk preferences. The planner’s objective is a two-stage utility functional where an outer utility function is applied to the distribution of the agents’ certainty equivalents from a given decision. Assuming lognormal risks and heterogeneous power utility preferences for the agents, we characterize optimal behavior in a setting where the planner can let each agent choose between different options from a fixed menu of possible decisions, leading to a grouping of the agents by risk preferences. These optimal decision menus are derived first for the case where the planner knows the distribution of preferences exactly and then for a case where he faces uncertainty about this distribution, only having access to upper and lower bounds on agents’ relative risk aversion. Finally, we provide tight bounds on the welfare loss from offering a finite menu of choices rather than fully personalized decisions.

中文翻译：

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通过确定性等价物为异构主体做出鲁棒决策

我们研究一个规划者的问题，他代表一群具有不同风险偏好的代理人来解决风险回报权衡（例如金融投资决策）。规划器的目标是一个两阶段效用函数，其中外部效用函数应用于给定决策中代理的确定性等价物的分布。假设代理的对数正态风险和异质电力效用偏好，我们在这样的环境中描述最佳行为：规划者可以让每个代理从固定的可能决策菜单中选择不同的选项，从而根据风险偏好对代理进行分组。这些最优决策菜单首先针对规划者确切知道偏好分布的情况得出，然后针对他面临该分布不确定性的情况得出，仅能访问代理人相对风险厌恶的上限和下限。最后，我们对因提供有限的选择菜单而不是完全个性化的决策而造成的福利损失提供了严格的限制。