A Survey on Gaps between Mean-Variance Approach and Exponential Growth Rate Approach for Portfolio Optimization

Portfolio optimization can be roughly categorized as the mean-variance approach and the exponential growth rate approach based on different theoretical foundations, trading logics, optimization objectives, and methodologies. The former and the latter are often used in long-term and short-term portfolio optimizations, respectively. Although the mean-variance approach could be applied to short-term portfolio optimization, the performance may not be satisfactory (same with the exponential growth rate approach to the long-term portfolio optimization). This survey mainly explores the gaps between these two approaches, and investigates what common ideas or mechanisms are beneficial. Besides, the evaluating framework of this field and some unsolved problems are also discussed.