Profile Evaluation and Help Needed for Research Interest in PhD. Statement of Purpose

Hi folks,

This is my first post here!

I am a mechanical engineering undergrad at a top-50 QS-ranked university entering my senior year in Hong Kong. Over the years, I realized that this major was not my cup of tea and I grew more inclined towards pursuing a career in a quant fund. Given my 3.32 cumulative GPA on a 4.3 scale ( I messed up really badly in my first two semesters with 2.86 and 3.2, followed by a 3.6, 3.9, and a 3.66 in the following semesters only to mess it all up with a 2.73 in my junior year's spring semester), I am adamant I won't get offers from most top MFE programs despite good quant scores in GRE mocks and having research affiliations with quant finance professors (one of which I aim to co-author with a professor and hope to publish in 12 months).

Thus, I decided I will be focusing on Ph.D. programs in applied mathematics in finance, or the Operations Research and Industrial/Information Engineering PhDs from good schools such as Columbia, Cornell, UC Berkeley (and some more) and focus on the domain of finance. My goal is to conduct my research and start as a quantitative researcher at a quant fund if I get into a good school for Ph.D., or a quant analyst if I get into a good MFE program.

Many of these doctoral programs require that I state my research interests in my statement of purpose, and highlight which professors I want to work with. I also want to apply to a couple of MPhil programs in Hong Kong for backup, and these universities encourage the applicants to propose a 2-3 page research plan with the application package.

I did read up some topics superficially, and I am really interested in stochastic volatility models. However, I doubt I can formulate a focused research idea having so little knowledge- after all, how much knowledge can I even gain after a couple of months of literature review?

I would really appreciate it if any of our quant veterans would suggest possible research topics, or shed some light on how much I should actually research and include in these statements of purpose and/or research proposals. Some opinions on my candidate profile would be nice too, both for MFE and Ph.D. programs.

Look forward to your ideas and suggestions.