Abstract: Trend representation index is an important topic in the field of portfolio optimization.However,most of the portfolio optimization systems based on trend representation only consider one index,and the effect of the system considering only one index is often quite different on different data sets,so we use multiple trend indices in our system.The portfolio optimization system proposed in this paper uses a series of radial basis functions corresponding to three trend representation indices (simple mo-ving average line,exponential moving average line and low-lag trendline) respectively.This system uses the above three indices and adds the peak price index according to the relationship between the closed price and the short-term average price.In this system,the series of radial basis functions will select the best trend expression index (adaptive selection) according to the recent investment situation.Then,the system will make investment according to the solution set of the convex optimization problem which aims at maximizing the wealth of the next period.Finally,the system and five common portfolio optimization systems are compared on two data sets,two of which are chosen to be compared in more detailed on four data sets,and we conclude that our system is better than other systems.

Key words: Exponential moving average line, Low-lag trendline, Peak price index, Portfolio optimization system, Radial basis functions