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

Battle Count: 90

The paper is primarily about preference recovery and welfare analysis rather than direct trading strategy development. However, it has significant indirect relevance: (1) understanding investor heterogeneity informs market microstructure and alpha generation; (2) transaction cost sensitivity recovery is directly applicable to execution algorithms; (3) dynamic regret bounds provide theoretical guarantees for adaptive portfolio management; (4) the finding that transaction-cost shocks dominate volatility shocks in welfare impact is actionable for risk managers; (5) ESG preference recovery supports sustainable investing strategies. The framework is more suited to portfolio managers and regulators than high-frequency traders.

The framework involves multiple layers of complexity: (1) solving forward quadratic programs via Gurobi; (2) implementing bilevel inverse optimization with KKT conditions; (3) grid-based parameter search over multi-dimensional preference space; (4) bootstrap confidence interval construction; (5) dynamic regret computation with temporal regularization; (6) distributionally robust reformulations (SOCP/SDP); (7) variational inequality formulations. The mathematical prerequisites include convex optimization, KKT theory, online learning, and robust optimization. However, the core implementation uses standard tools (CVXPY, OSQP, Gurobi) and the grid-based approach avoids complex gradient-based bilevel solvers.

The paper provides detailed experimental setup (Table 1), fixed random seeds, specific software versions (Gurobi 11.0, CVXPY 1.4.2, OSQP, Python 3.10), and mentions code availability via a private Kaggle repository. However, the code is only available 'upon reasonable request' and the Kaggle repository is private. The mathematical formulations and proofs are fully detailed in appendices. Monte Carlo protocol is clearly described with 7-step pipeline.