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Equilibrium investment with random risk aversion

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  • Sascha Desmettre
  • Mogens Steffensen

Abstract

We solve the problem of an investor who maximizes utility but faces random preferences. We propose a problem formulation based on expected certainty equivalents. We tackle the time‐consistency issues arising from that formulation by applying the equilibrium theory approach. To this end, we provide the proper definitions and prove a rigorous verification theorem. We complete the calculations for the cases of power and exponential utility. For power utility, we illustrate in a numerical example that the equilibrium stock proportion is independent of wealth, but decreasing in time, which we also supplement by a theoretical discussion. For exponential utility, the usual constant absolute risk aversion is replaced by its expectation.

Suggested Citation

  • Sascha Desmettre & Mogens Steffensen, 2023. "Equilibrium investment with random risk aversion," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 946-975, July.
    • Handle: RePEc:bla:mathfi:v:33:y:2023:i:3:p:946-975
    DOI: 10.1111/mafi.12394
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    References listed on IDEAS

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    Cited by:

    1. Balter, Anne G. & Schweizer, Nikolaus, 2024. "Robust decisions for heterogeneous agents via certainty equivalents," European Journal of Operational Research, Elsevier, vol. 317(1), pages 171-184.
    2. Luca De Gennaro Aquino & Sascha Desmettre & Yevhen Havrylenko & Mogens Steffensen, 2024. "Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time," Papers 2407.16525, arXiv.org, revised Oct 2024.
    3. Keffert, Henk, 2024. "Robo-advising: Optimal investment with mismeasured and unstable risk preferences," European Journal of Operational Research, Elsevier, vol. 315(1), pages 378-392.

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