Constructing Optimal Portfolio Rebalancing Strategies with a Two-Stage Multiresolution-Grid Model

Sophisticated predetermined ratios are used to allocate portfolio asset weights to strike a good trade-off between profitability and risk in trading. Rebalancing these weights due to market fluctuations without incurring excessive transaction costs and tracking errors is a vital financial engineering problem. Rebalancing strategies can be modeled by discretely enumerating portfolio weights to form a grid space and then optimized via the Bellman equation. Discretization errors are reduced by increasing the grid resolution at the cost of increased computational time. To minimize errors with constrained computational resources (e.g., grid nodes), we vary the grid resolution according to the probability distribution of asset weights. Specifically, a grid space is first divided into several areas, and each area’s probability is estimated. Then, the discretization error’s upper bound is minimized by inserting an adequate number of grid nodes determined by Lagrange multipliers in a non-uniform fashion. In experiments, the proposed multiresolution rebalancing outperforms traditional uniform-resolution rebalancing and popular benchmark strategies such as the periodic, tolerance-band, and buy-and-hold strategies.