Use of Mathematics in Stock Market

Source abstract

Stock market plays a key role in economical and social organization of a country. Stock market forecasting is highly demanding and most challenging task for investors, professional analyst and researchers in the financial market due to highly noisy, nonparametric, volatile, complex, non-linear, dynamic and chaotic nature of stock price time series. Prediction of stock market is a crucial task and prominent research area in financial domain as investing in stock market involves higher risk. However with the development of computational intelligent methods it is possible to reduce most of the risk. In this survey paper, our focus is on application of computational intelligent approaches such as artificial neural network, fuzzy logic, genetic algorithms and other evolutionary techniques for stock market forecasting. This paper presents an up-to-date survey of existing literature on stock market forecasting based on computational intelligent methods. The key result is that the probability distribution function of market timing returns is asymmetric, that the highest probability outcome for market timing is a below median return. Put another way, simple math says market timing is more likely to lose than to win—even before accounting for costs. The median of the market timing return probability distribution can be directly calculated as a weighted average of the returns of the model assets with the weights given by the fraction of time each asset has a higher return than the other. For the time period of the data the median return was close to, but not identical with, the return of a static 60:40 stock: