Inverse Portfolio Optimization with Synthetic Investor Data: Recovering Risk Preferences under Uncertainty

This study develops an inverse portfolio optimization framework for recovering latent investor preferences including risk aversion, transaction cost sensitivity, and ESG orientation from observed portfolio allocations. Using controlled synthetic data, we assess the estimator's statistical properties such as consistency, coverage, and dynamic regret. The model integrates robust optimization and regret-based inference to quantify welfare losses under preference misspecification and market shocks. Simulation experiments demonstrate accurate recovery of transaction cost parameters, partial identifiability of ESG penalties, and sublinear regret even under stochastic volatility and liquidity shocks. A real-data illustration using ETFs confirms that transaction-cost shocks dominate volatility shocks in welfare impact. The framework thus provides a statistically rigorous and economically interpretable tool for robust preference inference and portfolio design under uncertainty.