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 language | English |
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Journal | Mathematical Finance |
Volume | 33 |
Issue number | 3 |
Pages (from-to) | 946-975 |
Number of pages | 30 |
ISSN | 0960-1627 |
DOIs | |
Publication status | Published - 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