Compiled a list of papers applying (algebraic) topology to finance at: https://blog.nus.edu.sg/wuchengyuan/topology-in-finance/
Interestingly, topology seems best at detecting financial crashes, but can also predict stock price movement, do clustering and classification of financial time series, and more.
This 3 minute video explains very well how algebraic topology (in particular persistent homology) can be applied to finance:
Chengyuan Wu 