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Robust Decisions for Heterogeneous Agents via Certainty Equivalents

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  • Anne G. Balter
  • Nikolaus Schweizer

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.

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  • Anne G. Balter & Nikolaus Schweizer, 2021. "Robust Decisions for Heterogeneous Agents via Certainty Equivalents," Papers 2106.13059, arXiv.org.
    • Handle: RePEc:arx:papers:2106.13059
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    References listed on IDEAS

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    1. Magnus Dahlquist & Ofer Setty & Roine Vestman, 2018. "On the Asset Allocation of a Default Pension Fund," Journal of Finance, American Finance Association, vol. 73(4), pages 1893-1936, August.
    2. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    3. David E. Bell, 1982. "Regret in Decision Making under Uncertainty," Operations Research, INFORMS, vol. 30(5), pages 961-981, October.
    4. Balter, Anne G. & Mahayni, Antje & Schweizer, Nikolaus, 2021. "Time-consistency of optimal investment under smooth ambiguity," European Journal of Operational Research, Elsevier, vol. 293(2), pages 643-657.
    5. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    6. Simon, Leo K. & Zame, William R., 1987. "Discontinous Games and Endogenous Sharing Rules," Department of Economics, Working Paper Series qt8n46v2wv, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    7. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    8. Francesco D’Acunto & Nagpurnanand Prabhala & Alberto G Rossi, 2019. "The Promises and Pitfalls of Robo-Advising," The Review of Financial Studies, Society for Financial Studies, vol. 32(5), pages 1983-2020.
    9. Benjamin Armbruster & Erick Delage, 2015. "Decision Making Under Uncertainty When Preference Information Is Incomplete," Management Science, INFORMS, vol. 61(1), pages 111-128, January.
    10. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 92(368), pages 805-824, December.
    11. Calvet, Laurent E. & Campbell, John Y & Gomes, Francisco & Sodini, Paolo, 2021. "The Cross-Section of Household Preferences," CEPR Discussion Papers 16105, C.E.P.R. Discussion Papers.
    12. Bjarne Astrup Jensen & Jørgen Aase Nielsen, 2016. "How suboptimal are linear sharing rules?," Annals of Finance, Springer, vol. 12(2), pages 221-243, May.
    13. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-872, July.
    14. Henrik Cronqvist & Richard H. Thaler, 2004. "Design Choices in Privatized Social-Security Systems: Learning from the Swedish Experience," American Economic Review, American Economic Association, vol. 94(2), pages 424-428, May.
    15. Alserda, Gosse A.G. & Dellaert, Benedict G.C. & Swinkels, Laurens & van der Lecq, Fieke S.G., 2019. "Individual pension risk preference elicitation and collective asset allocation with heterogeneity," Journal of Banking & Finance, Elsevier, vol. 101(C), pages 206-225.
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    Cited by:

    1. Sascha Desmettre & Mogens Steffensen, 2023. "Equilibrium investment with random risk aversion," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 946-975, July.

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