An Improved Differential Evolution Algorithm And Its Application In Index Tracking

Index tracking model can be treated as an high-dimension nonlinear mixed-integer optimization problem, an global optimization problem , which is difficult to solve.An improved Differential evolution algorithm is developed to solve the high-dimension nonlinear mixed-integer optimization problem ,based on the original differential evolution algorithm . By using rand mutational coefficient, we improved the ability to escape from local optimal solution. Further, mixed-integer coding makes it possible to solve the mixed-integer optimal problem; we raise working efficiency by dropping the dimensions of the problem; we solve the problem, selecting an appropriate penalize coefficient which is difficult, by introducing double-selection- mechanism.A compact index tracking model is developed based on the thinking of Markowitz. The model is constructed using the close price of HS300 index,shangzheng 50 index and their corresponding stocks, and is solved by the improved differential evolution algorithm, which is feasible and effective for high-dimension mixed-integer nonlinear optimization problem. The result indicates that the differential evolution algorithm is feasible for the index tracing problem and the compact index tracking model can guarantee a positive stable bias compared with the corresponding index when a high skewness is accessible.A positive stable bias is useful for the alpha arbitrage and the enhanced fund management. The alpha arbitrage strategy and the enhanced fund management strategy based on the compact index tracking model can make excess return for investors.