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Career advice for econ major with hunger of math

Joined
1/30/22
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I'm fifth-year senior at an undergrad. economics program in an average (at best) university in South America. I'm enrolled in the program with a focus in corporate finance. My GPA at the end of the program will be in the neighborhood of 3.4/4 (or 4.3 out of 5). Took classes on mathematical economics (from several variable calculus to control theory, from a very application-first perspective, i.e. no real analysis only the "algorithms" used to solve particular problems), statistics I and II (up to application-first hypothesis testing), econometrics I and II (cross-section, time series, and bit of panel data). Also two classes on R and Python, both with the aim of using machine learning libraries.

In my fourth-year I took an elective class on optimization methods in finance and economics, which was meant to teach from a very basic, and intuition-first perspective, the math involved behind optimization in econ and quant-fin problems, ending up with an explanation of what stochastic calculus is. I absolutely loved it. Parallel to that, I was writing my thesis, on which I built a DSGE model, based on previous works, for assessing the impacts of a novel type of money on the economy. I mentioned this since it required me to study somewhat (for me) advanced topics by myself, and made me realize modelling and researching is a lot of fun for me. Also this work involved a lot of "programming" (using Matlab for numerical computations and optimizations) and applied calculus (finding closed-form first order conditions of simple dynamic programs).

With this two things in mind, making a career projection, I would really like to work researching in quantitative finance. Nonetheless as you may have already inferred, the mathematical tools I got from my econ major are not enough for what it takes for a job in this industry. Now the path is clear, a graduate level degree in applied math, financial engineering, mathematical finance, or related. Now, my question would be, what could I start doing right now in order to increase my chances to get info a good grad. program in the US or Europe in a couple of years?

I'm aware which kind of mathematical knowledge is expected of me to have, which would be: Real analysis -> measure-theoretic probability -> stochastic calculus and statistics (rigorous). I have already started self-studying fundamental logics and proofs, in order to follow the path from real analysis. I wanted to study it anyway, but how can I make it count for an application to grad. school?

On the programming side, I already am proficient in R and Python, and have very basic knowledge of C++. Again, what can I do to show my ability?

Probably worth mentioning, this last year of my undergrad. program I'm required to work in a six months internship, but I don't know which roles would be best for improving my quantitative background, since most folks of my program tend to go for Excel-monkey positions at banks or public ministries. I have been thinking of leveraging from my knowledge on DSGE models and trying to get a position at my country's central bank, since then I would probably have the opportunity to research and expanding my knowledge in some interesting areas like bayesian methods, that could somewhat help my in my quant path. Since the alternative would be working probably at fin making excel and pp, but at a very reputable institution (like citi or similar). Which would be better: reputable institution making corp. finance or researching on DSGE at a central bank?

Well I think that's all the relevant information I can provide you. Excuse me if this is overly asked, too long or a bit confusing (still perfectioning my English).

Thank you!
 
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