Equilibrium Investment with Random Risk Aversion

24 Pages Posted: 17 Mar 2021 Last revised: 28 Sep 2022

See all articles by Sascha Desmettre

Sascha Desmettre

Johannes Kepler University Linz

Mogens Steffensen

University of Copenhagen

Date Written: March 15, 2021


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 proof 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 optimal stock proportion is independent of wealth, but decreasing in timetime, which we also supplement by a theoretical discussion. For exponential utility, the usual constant absolute risk aversion is replaced by its expectation.

Keywords: Certainty equivalents, Random risk aversion, Time-inconsistency, Equilibrium approach, Power and Exponential utility

Suggested Citation

Desmettre, Sascha and Steffensen, Mogens, Equilibrium Investment with Random Risk Aversion (March 15, 2021). Available at SSRN: https://ssrn.com/abstract=3805069 or http://dx.doi.org/10.2139/ssrn.3805069

Sascha Desmettre (Contact Author)

Johannes Kepler University Linz ( email )

Altenbergerstr. 69
A-4040 Linz, Upper Austria 4040

HOME PAGE: http://shorturl.at/dwX47

Mogens Steffensen

University of Copenhagen ( email )

Universitetsparken 5
DK-2100 Copenhagen

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