Equilibrium investment under dynamic preference uncertainty

Paper: arXiv 2512.21149

Authors: Luca De Gennaro Aquino, Sascha Desmettre, Yevhen Havrylenko, Mogens Steffensen

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly sophisticated theoretical framework using an extended HJB system and coupled nonlinear PIDEs to solve dynamic portfolio choice under preference uncertainty. However, it is primarily mathematical and conceptual, relying on neural-network numerical approximations rather than empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A["Research Question: How do uncertain future preferences affect optimal dynamic portfolio choice?"] --> B["Inputs: Continuous-time asset returns & state-dependent CRRA utility driven by Itô diffusion"]
    B --> C["Aggregated Utility: Terminal wealth converted to Certainty Equivalents & nonlinearly aggregated (Time-Inconsistent)"]
    C --> D["Game-Theoretic Formulation: Develop extended HJB system for subgame-perfect equilibrium policies"]
    D --> E["Semi-Explicit Solution: Derive coupled nonlinear PIDE solved under Arithmetic Brownian Motion"]
    E --> F["Key Outcome: Investment policy decomposes into Myopic Demand + Novel Preference-Hedging Component"]

Cited References (115)

1. Backward stochastic differential equations in finance (1997)
2. Equilibrium portfolio selection for smooth ambiguity preferences (2025)
3. Risk aversion under preference uncertainty (2012)
4. Ambiguity, Risk, and Asset Returns in Continuous Time (2002)
5. A Regular Equilibrium Solves the Extended HJB System (2019)
6. Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework (1989)
7. Recursive smooth ambiguity preferences (2009)
8. Ambiguity, Learning, and Asset Returns (2012)

1 of 115 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.