In Jan., I will be starting a PhD in Applied Mathematics at the Colorado School of Mines. However, I was thinking about pursuing a MS in Financial Math afterwards. Would that be complete overkill or a good idea?
I agree, besides, a Ph.D is quite long, you can take course and self-learn all you'll learn in MS in the meanwhile.
You'll be doing a Ph.D in applied math , financial mathematics easily falls in that category so I see no need to do the same thing twice.