Robust decisions for heterogeneous agents via certainty equivalents
研究一个规划者如何为具有不同风险偏好的群体设计有限选项菜单，以在风险-收益权衡中做出稳健决策，并量化菜单与完全个性化决策的福利损失。
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.