Portfolio Optimization

Portfolio optimization studies how to allocate money across assets while balancing expected returns against risk, diversification, and practical limits such as transaction costs or position caps. Classical approaches include mean-variance optimization, risk-parity, and CVaR-based methods; newer work also uses robust optimization, improved covariance estimates, and evolutionary algorithms to handle uncertainty and complex constraints. Machine learning methods predict returns and risks, learn weights end to end, or use reinforcement learning to adapt allocations over time, sometimes incorporating market regimes or investor preferences. A central challenge is that better forecasts or backtest results do not necessarily produce reliable gains after costs, across changing markets, and under realistic out-of-sample evaluation.