Equilibrium investment with random risk aversion

Sascha Desmettre*, Mogens Steffensen

*Corresponding author for this work

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4 Citations (Scopus)
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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.

Original languageEnglish
JournalMathematical Finance
Volume33
Issue number3
Pages (from-to)946-975
Number of pages30
ISSN0960-1627
DOIs
Publication statusPublished - 2023

Bibliographical note

Publisher Copyright:
© 2023 The Authors. Mathematical Finance published by Wiley Periodicals LLC.

Keywords

  • certainty equivalents
  • equilibrium approach
  • power and exponential utility
  • random risk aversion
  • time-inconsistency

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