Single-Period Portfolio Selection via Information Projection
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910204483862528 |
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| author | Yang, Bo-Yu Gastpar, Michael |
| author_facet | Yang, Bo-Yu Gastpar, Michael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03184 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Single-Period Portfolio Selection via Information Projection Yang, Bo-Yu Gastpar, Michael Information Theory Mathematical Finance Portfolio Management 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. |
| title | Single-Period Portfolio Selection via Information Projection |
| topic | Information Theory Mathematical Finance Portfolio Management |
| url | https://arxiv.org/abs/2605.03184 |