Robust Decisions for Heterogeneous Agents via Certainty Equivalents

35 Pages Posted: 8 Jul 2021

See all articles by Anne Balter

Anne Balter

Tilburg University; Netspar

Nikolaus Schweizer

Tilburg School of Economics and Management

Date Written: June 24, 2021

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.

Suggested Citation

Balter, Anne and Schweizer, Nikolaus, Robust Decisions for Heterogeneous Agents via Certainty Equivalents (June 24, 2021). Available at SSRN: https://ssrn.com/abstract=3873267 or http://dx.doi.org/10.2139/ssrn.3873267

Anne Balter (Contact Author)

Tilburg University ( email )

P.O. Box 90153
Tilburg, DC Noord-Brabant 5000 LE
Netherlands

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Nikolaus Schweizer

Tilburg School of Economics and Management ( email )

PO Box 90153
Tilburg, 5000 LE Ti
Netherlands

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