PhD Program from target school

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I am a junior in math at a target school (one of MIT, Berkeley, CMU), but I have only recently settled on going for a position in quantitative finance (preferably researcher). I still want to do a math PhD but I was wondering if I should go for another direction. My primary interest in math right now is discrete mathematics/theoretical CS, both of which don't seem to be involve very relevant skillsets for quant. Except maybe they train you well for brainteasers, but doing a phd for brainteasers seem overkill. Are there any directions/programs that quant firms like to hire researchers from? I know that the competition for a phd program is much tougher than undergrad and I may not be a competitive candidate for the top math phd programs. Do firms still hire lower tier phds? I am open to suggestions of programs outside of the US as well.

Information about me: I have a good gpa but no good research currently, and I am trying to place decently on the Putnam, if that would help with grad school. I also have some high school recognitions like USAMO that helped me get into college but presumably won't help much with grad school.

Any advice appreciated.
 
As someone who went through the same Math PhD process (number theory specifically), I would say that doing a math PhD for the sole purpose of getting a job in finance is a long, hard and may not be optimal path to get there.
As you are still a junior in college, there are times for you to identify hard skills (definitely coding C++, Python, dataset), tune up your resume and interview practice. If you know what you want to do, it's better to focus the time on strengthen the skills and do all the prep works to get you ahead of the competition.
You are from a target school so you have a better shot of getting at least a first round interview or OA (online assessment). The rest is up to your preparation that I lay out above.
Here is a helpful guide by @Ash Cross
 
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