Good Ph.D. programs after MS in financial engineering?

Hi, I am still in my undergraduate years looking to apply to a MS in financial engineering next year with my eyes on the Columbia and Berkley programs. Although the road is still long, I am looking for a good PhD program to look into after graduation from the MS in financial engineering. A bit about myself for background: I am a senior at a US college studying mathematics, computer, and information science with a concentration in financial programing. I plan to pursue a career in either derivatives trading, HFT, or risk management.

which of the following PhDs would you suggest, I would love to hear specific tracks or programs:
1- PhD in Physics
2- PhD in mathematics
3- PhD in computer science
 
I would say best route is go for phd in OR at Columbia get the masters for free and go from there. Or there MS is a good option which will be cheaper
Completely agree with @Michsund here. You could also go with OR from MIT, IEOR from Berkeley, or ORFE from Princeton to name a few other OR PhD programs. Also, if you plan on doing a PhD at one of the super elite OR programs, it's best to get some research experience. With that in mind, I'm not sure if UCB's MFE program is appropriate in the sense that you get time to do academic research--I could be completely wrong, perhaps you can use the time for the internship to do research with faculty? Maybe UCB MFE students can shed more light here?
which of the following PhDs would you suggest, I would love to hear specific tracks or programs:
1- PhD in Physics
2- PhD in mathematics
3- PhD in computer science
In all honesty, I think all are fine. I would suggest beefing up on computer science / DS&A courses if the specific program doesn't provide sufficient exposure.
 
I would like to pursue a career in Quantitative Research - Pricing researchers, Algorithmic developers for high-frequency trading or broking firms, Strategy researcher. I plan to complete my 4-year undergraduate degree in mathematics, computer, and information science followed by MS in FE directly after it. Later, I would like to work on a part-time Ms in machine learning (thoughts on instead taking Ms in applied math, finance, software engineering would be appreciated) I will do so to gather the work experience before attending a deferred MBA program. Finally, after completing all programs I would like to do a Ph.D.

Ph.D. in Operations Research and FE sounds very interesting and was my top choice but I am worried about the negative effect given I am already doing a Ms in FE (ofc a Ph.d doesn't compare to a Ms in FE ). The same thought applies to Financial Mathematics programs.
Mathematics Ph.d: I have my eye on applied mathematics but combinatorics is also on my radar would love to hear your recommendations.
For physics and computer science, I don't have anything specific program in mind but I noticed the influx of physics Ph.D. holders specifically in the field interested me, and I am hoping to get thoughts on that too if possible.

At the end of the road, I hope to have a career in quant hedge funds, not academic work. I know thinking about which Ph.D. is early considering I am yet to finish my undergraduate, but I would like to have completed any prerequisites.
 
Completely agree with @Michsund here. You could also go with OR from MIT, IEOR from Berkeley, or ORFE from Princeton to name a few other OR PhD programs. Also, if you plan on doing a PhD at one of the super elite OR programs, it's best to get some research experience. With that in mind, I'm not sure if UCB's MFE program is appropriate in the sense that you get time to do academic research--I could be completely wrong, perhaps you can use the time for the internship to do research with faculty? Maybe UCB MFE students can shed more light here?

In all honesty, I think all are fine. I would suggest beefing up on computer science / DS&A courses if the specific program doesn't provide sufficient exposure.
Thank you both for the advice, greatly appreciated. Someone, please correct if wrong but I believe the USB MFE has either an internship or research requirements.

To pursue an elite Ph.D program would you suggest it's recommended to take a second Ms from any of the quant fields or would you suggest MSFE would be sufficient?
 
To pursue an elite Ph.D program would you suggest it's recommended to take a second Ms from any of the quant fields or would you suggest MSFE would be sufficient?
I think MSFE (or even an OR MS) is sufficient as long as it's from one of the top MFE programs like CMU MSCF and Columbia MSFE. Just make sure you work on some good research with faculty so that they can vouch for you--even better if you can get something published! A strong recommendation from faculty at the top schools/programs holds much more weight than a strong recommendation from faculty at low-tier schools/programs given all else equal. I would also suggest taking PhD level coursework (PhD courses at top PhD programs are much, much harder than their equivalents at low-ranking PhD programs) and doing well in those.
 
Since a background in math finance is not useful in a PhD program in the fields you listed, an MS in Math Finance would not help you get into a PhD program. If you really want to get a PhD, then it's best to take the most challenging courses now in one of the areas. And maybe try to do some undergraduate research. Put aside the math finance for now. If you do get a PhD, learning the finance will be quick and easy afterwards. You can enter an MS program after you get a PhD.

A PhD program is quite intense, so you should do it only if you really really like and are good at the area you choose. If you have no particular interest in doing research in math, CS, or physics and want the PhD only as a credential to become a quant, then it's not likely to work out well.
 
Since a background in math finance is not useful in a PhD program in the fields you listed, an MS in Math Finance would not help you get into a PhD program.
In general, I agree with this. But I do think if you do the MS in Math Finance in a top program and have done excellent in PhD courses (on par with those from a top PhD program of course) and/or published--not just done research, you should have a strong chance. I've seen a CMU MSCF student get into Columbia IEOR PhD and a Columbia MSFE student get into Princeton ORFE PhD though I think they all had strong math backgrounds from undergrad.
If you really want to get a PhD, then it's best to take the most challenging courses now in one of the areas.
And hopefully on par with the difficulty of the PhD courses from your target PhD program. I'm sure Courant math PhD courses are much more harder than math PhD courses from a relatively unknown program in a relatively unknown university lol
And maybe try to do some undergraduate research.
If you're coming from a mediocre undergrad program, I think you really need to publish. Not saying doing undergraduate research is easy, but a publication holds much more weight and credentials than just doing research. Assuming you do a very good job, I think it also helps if your undergraduate research supervisor is famous/well-known in your field of interest...yes, there's unfortunately some politics involved, not just in industry lol.
 
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