Robust Decisions for Heterogeneous Agents via Certainty Equivalents

TL;DR

This paper develops a framework for a planner to make optimal risk-return decisions for heterogeneous agents with different risk preferences, using certainty equivalents and utility functions, under both known and uncertain preference distributions.

Contribution

It introduces a method to determine optimal decision menus for agents with diverse risk preferences, accounting for uncertainty in preference distribution.

Findings

Optimal decision menus depend on agents' risk preferences and available information.

Tight bounds on welfare loss are derived for finite decision menus.

The approach handles both known and uncertain preference distributions.

Abstract

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.