Mathematics underlying the 2008 financial crisis, and a possible remedy

There are a few serious problems with this. First, this could also have the adverse result of making the eventual collapse even worse. I think that it is much easier to handle less serious but more frequent collapses, as opposed to the Great Depression once a decade.

Second, there's a reason states don't print their own currency and the EU has adopted a common currency: it makes economic coordination so much more efficient. If each state had its own currency we would waste efficiency constantly exchanging currency, and out of state business would become subject to the volatile exchange fund market. Sure, this idea may solve one problem, but it certainly creates many more.