Portfolio Optimization in the Stock Market

The portfolio optimization problem involves selecting and allocating resources among a set of financial assets to achieve specific investment objectives. The most common goal is to maximize returns while minimizing risk, typically measured by variance or standard deviation.

This problem is governed by constraints such as budget limits, investment proportions, transaction costs, or regulatory requirements. In mathematical terms, it often involves optimizing a utility function (e.g., expected returns minus a penalty for risk) under constraints like:

• Budget constraint: Total allocation equals available capital.
• Non-negativity: Proportions must be non-negative (long-only portfolios).
• Diversity constraints: Limiting over-concentration in specific assets.

Classic approaches include Markowitz's mean-variance optimization, risk-parity strategies, and more advanced methods like robust optimization and machine learning-based techniques for dynamic adjustments.

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