May I submit reading anything by William Bernstein to anyone interested in a math-heavy discussion of this? The book "the intelligent asset allocator" is the most math heavy of the set.

His best quote on this is "assume a very fat tail" i.e. assume statistically unlikely events are rather likely as a group.

I would also like to take a moment to praise Alexander Hamilton and his friends for setting the precedent that the US has never defaulted. We were awfully close after the revolutionary war.