On consistency of optimal portfolio choice for state-dependent exponential utilities

Paper: arXiv 2501.01748

Authors: Edoardo Berton, Marzia De Donno, Marco Maggis

Abstract

In an arbitrage-free simple market, we demonstrate that for a class of state-dependent exponential utilities, there exists a unique prediction of the random risk aversion that ensures the consistency of optimal strategies across any time horizon. Our solution aligns with the theory of forward performances, with the added distinction of identifying, among the infinite possible solutions, the one for which the profile remains optimal at all times for the market-adjusted system of preferences adopted.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical exploration of time-consistent portfolio choice under stochastic risk aversion using stochastic calculus and martingale methods. However, it is purely mathematical finance with no empirical backtesting, real data validation, or code provided.

Research Flowchart

  flowchart TD
    A[Goal: Consistent Optimal Strategy<br/>Across Any Time Horizon] --> B[Input: Arbitrage-Free Market &<br/>State-Dependent Exponential Utilities]
    B --> C[Method: Apply Forward Performance Theory<br/>& Stochastic Optimal Control]
    C --> D[Compute: Characterize Class of<br/>Random Risk Aversion Profiles]
    D --> E[Outcome: Unique Prediction of Risk Aversion<br/>Ensuring Time-Consistent Portfolio Choice]