Equilibrium investment with random risk aversion
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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.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Mathematical Finance |
| Vol/bind | 33 |
| Udgave nummer | 3 |
| Sider (fra-til) | 946-975 |
| Antal sider | 30 |
| ISSN | 0960-1627 |
| DOI | |
| Status | Udgivet - 2023 |
Bibliografisk note
Funding Information:
We wish to thank two anonymous referees for constructive suggestions that greatly helped to improve the paper. Lukas Wögerer provided assistance for the implementation of the numerical example. S. Desmettre is supported by the Austrian Science Fund (FWF) project F5507-N26, which is part of the Special Research Program Quasi-Monte Carlo Methods: Theory and Applications.
Funding Information:
We wish to thank two anonymous referees for constructive suggestions that greatly helped to improve the paper. Lukas Wögerer provided assistance for the implementation of the numerical example. S. Desmettre is supported by the Austrian Science Fund (FWF) project F5507‐N26, which is part of the Special Research Program . Quasi‐Monte Carlo Methods: Theory and Applications
Publisher Copyright:
© 2023 The Authors. Mathematical Finance published by Wiley Periodicals LLC.
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