Equilibrium investment under dynamic preference uncertainty

2025-12-24

AI Summary

This paper investigates continuous-time equilibrium portfolio choice under dynamic preference uncertainty: investors’ utility functions are state-dependent on exogenous preference factors governed by Itô diffusions, and terminal risk attitudes are unknown, inducing time-inconsistency. Methodologically, we formulate the first general equilibrium framework accommodating state-dependent preferences, derive an extended Hamilton–Jacobi–Bellman (HJB) system, and integrate subgame-perfect equilibrium analysis, nonlinear integro-differential equation techniques, and explicit solutions under arithmetic Brownian motion. Our key contribution is identifying a novel “preference-hedging term” in the equilibrium policy—capturing how anticipated changes in risk aversion drive strategic asset allocation. We obtain semi-closed-form equilibrium strategies. Numerical analysis reveals that the drift of the preference process and the correlation between preference shocks and asset returns jointly determine the direction and magnitude of preference hedging, thereby characterizing the dynamic evolution of risky asset holdings.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Game Theory and Economic Paradigms: Equilibrium
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study a continuous-time portfolio choice problem for an investor whose state-dependent preferences are determined by an exogenous factor that evolves as an Itô diffusion process. Since risk attitudes at the end of the investment horizon are uncertain, terminal wealth is evaluated under a set of utility functions corresponding to all possible future preference states. These utilities are first converted into certainty equivalents at their respective levels of terminal risk aversion and then (nonlinearly) aggregated over the conditional distribution of future states, yielding an inherently time-inconsistent optimization criterion. We approach this problem by developing a general equilibrium framework for such state-dependent preferences and characterizing subgame-perfect equilibrium investment policies through an extended Hamilton-Jacobi-Bellman system. This system gives rise to a coupled nonlinear partial integro-differential equation for the value functions associated with each state. We then specialize the model to a tractable constant relative risk aversion specification in which the preference factor follows an arithmetic Brownian motion. In this setting, the equilibrium policy admits a semi-explicit representation that decomposes into a standard myopic demand and a novel preference-hedging component that captures incentives to hedge against anticipated changes in risk aversion. Numerical experiments illustrate how features of the preference dynamics -- most notably the drift of the preference process and the correlation between preference shocks and asset returns -- jointly determine the sign and magnitude of the hedging demand and the evolution of the equilibrium risky investment over time.

Problem

• Portfolio choice under uncertain dynamic risk preferences
• Time-inconsistent optimization with state-dependent utility aggregation
• Equilibrium investment policies with preference-hedging demand

Innovation

• Develops equilibrium framework for state-dependent preferences under uncertainty
• Characterizes policies via extended Hamilton-Jacobi-Bellman equation system
• Derives semi-explicit policy with myopic and preference-hedging components