What are the prospects of a Math Master student applying to Finance PhD programs?
Admissions for PhD programs at top-tier schools is hyper competitive, and I would imagine it to be even more for finance and economy. Admissions there get huge pools of applicants and they are spoiled in their choices. Applicants would come with these perfect GPA and GRE scores and crafted portfolios from top-tier undergrad programs and so on.

I would say, though, that you can apply and see. But do not limit yourself with top tier universities! You can always find 2nd-tier ones with fantastic research groups in some specific areas that might be of your interest. Do NOT choose where you want to do PhD solely based on the reputation of the university. There is more to it than that, you have to see the research group and their reputation and what journals/conferences they publish in, etc...

Also, here is a link for you to read. You might find it to be such a treat.
http://noahpinionblog.blogspot.com/2013/05/if-you-get-phd-get-economics-phd.html