Single-Period Portfolio Selection via Information Projection

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 R\'enyi divergence term, a R\'enyi entropy term of the risk-tilted market law, and a log-partition term. In this setting, the R\'enyi 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 R\'enyi information-projection problem. Using a variational representation of R\'enyi 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.