Dynamic portfolio selection under generalized disappointment aversion

ArXiv ID: 2401.08323 “View on arXiv”

Authors: Unknown

Abstract

This paper addresses the continuous-time portfolio selection problem under generalized disappointment aversion (GDA). The implicit definition of the certainty equivalent within GDA preferences introduces time inconsistency to this problem. We provide the sufficient and necessary condition for a strategy to be an equilibrium by a fully nonlinear integral equation. Investigating the existence and uniqueness of the solution to the integral equation, we establish the existence and uniqueness of the equilibrium. Our findings indicate that under disappointment aversion preferences, non-participation in the stock market is the unique equilibrium. The semi-analytical equilibrium strategies obtained under the constant relative risk aversion utility functions reveal that, under GDA preferences, the investment proportion in the stock market consistently remains smaller than the investment proportion under classical expected utility theory. The numerical analysis shows that the equilibrium strategy’s monotonicity concerning the two parameters of GDA preference aligns with the monotonicity of the degree of risk aversion.

Keywords: Generalized Disappointment Aversion, Time Inconsistency, Equilibrium Strategies, Portfolio Selection, Non-participation, Equities

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is highly theoretical, featuring a fully nonlinear integral equation and proofs of existence/uniqueness, warranting a high math complexity score. However, it contains no backtesting, datasets, or statistical metrics, and is purely analytical, resulting in a very low empirical rigor score.

  flowchart TD
    subgraph A ["Research Goal"]
        A1["Continuous-time portfolio selection<br>under Generalized Disappointment Aversion<br>to address time inconsistency"]
    end

    subgraph B ["Methodology & Analysis"]
        B1["Derive fully nonlinear integral equation<br>for equilibrium condition"]
        B2["Analyze existence & uniqueness<br>of solution"]
    end

    subgraph C ["Key Findings"]
        C1["Unique Equilibrium: Non-participation<br>in stock market"]
        C2["Investment proportion in stocks<br>consistently lower than EUT"]
        C3["Monotonicity aligns with<br>risk aversion degree"]
    end

    A --> B
    B --> C