Paper: arXiv 2605.03184

Authors: Bo-Yu Yang, Michael Gastpar

Abstract

We study the single-period portfolio selection problem under Constant Relative Risk-Aversion (CRRA) utility through the information-theoretic lens. Assuming only that the market payoff vector has finite support, we show that the Certainty-Equivalent (CE) growth rate under CRRA utility can be decomposed into a portfolio-induced Rényi divergence term, a Rényi entropy term of the risk-tilted market law, and a log-partition term. In this setting, the Rényi order has a clear operational meaning: it exactly coincides with the investor’s coefficient of relative risk aversion. We further show that CRRA portfolio selection is equivalent to a Rényi information-projection problem. Using a variational representation of Rényi divergence, we obtain a Blahut-Arimoto-style alternating optimization with a closed-form auxiliary update and a KL-type portfolio step. In the low risk-aversion regime, this method empirically requires fewer iterations than both direct CRRA utility optimization and Cover’s method.

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 relies on advanced information-theoretic constructs, including Rényi divergence, Blahut-Arimoto alternating optimization, and information projection geometry to derive a theoretical optimization framework. While it provides an empirical comparison of iteration counts, it lacks extensive backtesting on real-world market datasets or transaction cost modeling, focusing primarily on the structural proof of the optimization equivalence.

Research Flowchart

  flowchart TD
    A[<b>Goal</b>: Optimize CRRA Portfolio via Information Theory] --> B[<b>Input</b>: Market payoffs with finite support]
    B --> C[<b>Methodology</b>: Decompose CE rate into Rényi divergence & entropy]
    C --> D[<b>Computational Process</b>: Blahut-Arimoto alternating optimization]
    D --> E[<b>Result</b>: Equivalent to Rényi information-projection]
    E --> F[<b>Finding</b>: Faster convergence in low risk-aversion regime]

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