Optimal information acquisition for eliminating estimation risk

Paper: arXiv 2405.09339

Authors: Zongxia Liang, Qi Ye

Abstract

This paper diverges from previous literature by considering the utility maximization problem in the context of investors having the freedom to actively acquire additional information to mitigate estimation risk. We derive closed-form value functions using CARA and CRRA utility functions and establish a criterion for valuing extra information through certainty equivalence, while also formulating its associated acquisition cost. By strategically employing variational methods, we explore the optimal acquisition of information, taking into account the trade-off between its value and cost. Our findings indicate that acquiring earlier information holds greater worth in eliminating estimation risk and achieving higher utility. Furthermore, we observe that investors with lower risk aversion are more inclined to pursue information acquisition.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using stochastic calculus, variational methods, and Bayesian learning to solve optimal information acquisition problems under CARA and CRRA utility. However, it is entirely mathematical and lacks empirical data, backtesting, or simulation studies.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Information Acquisition to Eliminate Estimation Risk] --> B[Inputs: CARA/CRRA Utilities, Multi-Asset Market Data & Cost Function]
    B --> C[Derive Closed-Form Value Functions via Certainty Equivalence]
    C --> D[Formulate Optimization Problem using Variational Methods]
    D --> E[Balance Information Value vs. Acquisition Cost]
    E --> F[Outcomes: Earlier Information is More Valuable; Lower Risk Aversion Drives Higher Acquisition]