As far as a beginners introduction, I have been using 'Computational Topology' by Edelsbrunner and Harer at Duke. We have spoken with John Harer about the application of persistent homology type things for other (non finance) problem sets. I think there is the possibility to, just as you say, use this to reduce model risk, with some caveats. For their time series processing, they do assume some complex cyclical behavior that can be estimated using a statistical view of persistent homology, and have applied it to biological systems. That would be better than a Markov process for finding and utilizing 'patterns', if they exist.
Last edited by ChristopherB
on September 2nd, 2013, 10:00 pm, edited 1 time in total.