By name: information-theoretic-portfolio-selection description: Portfolio selection methodology using information projection and Renyi divergence decomposition under CRRA utility. Decomposes certainty-equivalent growth rate into portfolio-induced Renyi divergence, Renyi entropy of risk-tilted market law, and log-partition term. Use when designing portfolio selection strategies, applying information theory to finance, optimizing under risk aversion, or analyzing market payoff distributions through divergence measures.
Information-Theoretic Portfolio Selection
Portfolio selection under CRRA utility through information-theoretic lens.
Core Theory
For a market with finite-support payoff vector, the CRRA certainty-equivalent growth rate decomposes as:
CE_growth = D_α(p_portfolio || p_market) + H_α(p_risk_tilted) + log(Z)
where:
D_α: Portfolio-induced Renyi divergence from market lawH_α: Renyi entropy of risk-tilted market distributionlog(Z): Log-partition function termα: Renyi order, operationally linked to risk aversion coefficient
Key Insight
The Renyi order α has clear operational meaning: it equals the investor's risk aversion parameter. This bridges information geometry with portfolio theory.
Methodology Steps
- Estimate Market Distribution: From historical returns, construct empirical payoff distribution
- Compute Risk-Tilted Law: p_α(x) ∝ p(x)^α (exponential tilting)
- Calculate Renyi Divergence: D_α between portfolio-induced and market distributions
- Optimize: Maximize CE_growth = divergence + entropy + log-partition
- Select Portfolio: Choose weights that maximize information-theoretic objective
Practical Applications
- Single-period portfolio selection
- Risk-aversion calibration via Renyi order
- Market efficiency assessment via divergence measures
- Information geometry approach to asset allocation
Activation
portfolio selection, CRRA utility, Renyi divergence, information projection, information theory finance, risk aversion optimization, market payoff distribution