Modeling Cascading Failures in Stock Markets by a Pretopological Framework

We introduce a computational framework, namely, a pretopological construct, for mining stock prices' time series in order to expand a set of stocks by adding other stocks whose average correlations with the set are above a threshold. We increase the threshold with the set's size to verify group impact in financial crises. This approach is tested by a consecutive expansion process started from a stock of Merrill Lynch & Co., and a consecutive contraction process of the rest. The test's results and the comparison to graph theory show that our model and pretopology theory are helpful to study stock markets.