A Minimax Diversification Approach to Dynamic Portfolio Optimization

This paper investigates a multi-period investment problem in which an investor revises investment decisions at the beginning of each period. The objective is to maximize expected terminal wealth while simultaneously minimizing risk. This study quantifies risk using a dynamic risk function grounded in the minimax risk diversification principle. A key feature of the model is its flexibility: in each period, the investor constructs the risk function using either standard deviation, absolute deviation, or lower semi-absolute deviation, thereby accommodating diverse risk preferences. By employing dynamic programming, analytical solutions for the optimal investment strategy are derived. These solutions explicitly demonstrate the strategy’s dependence on the expected return rates of risky assets and the investor’s risk tolerance.