Multi-Period Portfolio Optimization Model with Cone Constraints and Discrete Decisions

This work develops a practical multi-period optimization approach that incorporates real-world constraints, including discrete decisions and conic risk constraints. Expanding upon earlier single-period models, our framework employs a binary scenario tree derived from monthly returns of randomly selected S&P 500 stocks to represent market evolution across multiple periods. The formulation captures essential portfolio constraints, such as transaction fees, sector diversification, and minimum investment thresholds, resulting in a robust and comprehensive optimization approach. To efficiently solve the resulting mixed-integer second-order cone programming (MISOCP) problem, we employ an outer approximation algorithm with a warmstart strategy, which significantly improves solution runtimes and computational efficiency. Numerical experiments demonstrate the model’s effectiveness, showing an average improvement of 10.71% in iteration count and 15.24% in computational time when using the warmstart approach.