Single-Period Portfolio Selection via Information Projection

2026-05-04

AI Summary

This study addresses the single-period portfolio selection problem under constant relative risk aversion (CRRA) utility in markets with finite support. From an information-theoretic perspective, it decomposes the certainty-equivalent growth rate into a Rényi divergence term, the Rényi entropy of a risk-tilted distribution, and a log-partition term. The work reformulates CRRA optimization as a Rényi information projection problem for the first time, establishing an exact correspondence between the Rényi order and the risk aversion coefficient. Leveraging the variational representation of Rényi divergence, the authors devise a Blahut–Arimoto–type alternating optimization algorithm featuring closed-form auxiliary variable updates and KL-divergence–based portfolio updates. Empirical results demonstrate that, particularly under low risk aversion, the proposed method converges faster and requires fewer iterations than both direct CRRA optimization and Cover’s universal portfolio strategy.

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 exactly 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.

Problem

• portfolio selection
• CRRA utility
• single-period
• Rényi divergence
• information projection

Innovation

• Rényi divergence
• information projection
• CRRA utility
• portfolio optimization
• Blahut-Arimoto algorithm