Abstract:  Since stock market bubbles are payed close attention by investors,it is meaningful to figure out the breakage time of the stock market bubble for investors to manage risks.In this paper by regarding the stock market bubbles as physical bubbles and taking into account the fluctuations of stock market,a model to depict the stock market bubbles is build.Parameters in the model are estimated by the least square method and genetic algorithm.Empirical analysis with our model on the Shanghai securities composite indexes of three time intervals shows that the errors between the predicted breakage time and the real breakage time of stock market bubbles are small,and furthermore,the time of the bubble breakage forecasted is more likely after the real breakage time.The model is used to forecast the Shanghai securities composite indexes from January,2014 to June,2015,and it is found that the predicted breakage time is almost the same to the real breakage time, which demonstrates that our bubble model has good effects in depicting the risks in stock market.

Key words:

Physical bubble, Stock market bubble, Risk, Mathematical model, Genetic algorithm