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Related Experiment Video

Updated: Jun 30, 2025

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

Equilibrium investment with random risk aversion.

Sascha Desmettre¹, Mogens Steffensen²

¹Institute for Financial Mathematics and Applied Number Theory University of Linz Linz Austria.

Mathematical Finance

|March 20, 2024

Summary

Investors with random preferences can maximize utility using expected certainty equivalents. This approach addresses time-consistency issues, with equilibrium stock proportions independent of wealth but decreasing over time for power utility.

Keywords:

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

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Area of Science:

Finance
Decision Theory
Mathematical Economics

Background:

Traditional investment models assume stable investor preferences.
Random preferences introduce complexities in utility maximization and decision-making.
Time-consistency is a critical challenge in dynamic financial planning.

Purpose of the Study:

To formulate and solve the problem of utility maximization under random preferences.
To address and resolve time-consistency issues in dynamic decision-making.
To analyze the behavior of investment strategies for specific utility functions.

Main Methods:

Formulation of the investment problem using expected certainty equivalents.
Application of equilibrium theory to ensure time-consistency.
Development of rigorous definitions and a verification theorem.
Analytical calculations for power and exponential utility functions.

Main Results:

The proposed formulation effectively handles random preferences.
Equilibrium theory successfully resolves time-consistency challenges.
For power utility, equilibrium stock proportion is wealth-independent and time-decreasing.
For exponential utility, constant absolute risk aversion is replaced by its expectation.

Conclusions:

The expected certainty equivalent approach provides a robust framework for investors with random preferences.
Equilibrium theory is a valid method for ensuring time-consistent strategies in dynamic settings.
The findings offer insights into optimal portfolio allocation under uncertainty and changing preferences.