# How math-heavy is graduate quantitative finance?

This post concerns grad school options. I am an undergraduate math major and will soon complete my studies. I am considering finance/financial engineering. How math-heavy is the financial mathematics compared to pure mathematics? Is it equally as challenging and tough?

Basically, I am considering finance because pure mathematics is rather challenging for me. If you need more clarification, mention in comments.

Programs vary; it would be best to look at the specific requirements and prerequisites for the programs you have in mind.

In general, mathematical finance can involve a very considerable amount of pure mathematics. A big piece is modeling assets via stochastic processes, and to understand those properly requires a firm background in graduate-level real analysis, measure theory, probability theory, and often functional analysis and PDE. A mathematical finance course may well consist primarily of theorems and proofs, just like a pure math course would. This is typically even more true at the PhD level than masters.

Of course, I would say that just because mathematics is challenging, that doesn't mean you should avoid it!

The reason I'm writing this in the form of an answer instead of a comment is because I can't write a short enough comment to meet the character restrictions. So, don't take this as an answer, as I don't intend it to be. You've just asked a pretty broad question.

Your question is awfully familiar in content and application to the very same question that I asked myself when entering into college to study computer science. I found out that it is true that computer science is very math heavy and a good solid foundation in math greatly helps; however, it's not in the way that people normally envision mathematics being used when they hear "math heavy."

One thing I will say is that while I'm not into graduate finance work, I've seen some graduate finance work as a programmer. Sure, there's math involved -- and lots of it. It's all math, numbers, and logic; but, then again, what isn't? People have said before that construction is very math oriented, and I'd agree with that to a point. Just like I found out with computer science, yes it's math heavy, but I'm not explicitly solving mathematical equations every second of every day. The familiarity with mathematics and mathematical intuition developed from doing mathematics, something I call mathematical maturity, really benefits the perspective that problems are viewed from. I think that applies to everything else, too. So, I think a familiarity with mathematics benefits all fields of study for people from all walks of life.

Courant is one of the top places in the world to get a MS in Finance. This is what their website says:

http://math.nyu.edu/financial_mathematics/content/05_prospectiveStudents/02.html

Basically, you will need to have some grasp of Stochastic Calculus, Probability Theory, and Numerical Analysis. Some knowledge of Functional Analysis and Real Analysis/Measure Theory will help with the proofs but for the most part, from the point of view of writing Models, coding them up, simulating them, and calibrating them you will mostly be solving PDEs. You'll probably use MATLAB or C++ .

Your program may also have a strong econometrics basis, so you will need to develop data skills and learn how to use packages like SAS, STATA, LIMDEP etc. The theory will involve some linear algebra and probability theory.

The professors may not go very deep into Finance Theory but the type of math they use there involves Functional Analysis, Dynamic Programming, Martingales etc.

The program will be fast paced and challenging, especially Finance Theory since you won't have a base for it but you should be fine with the math part of it if you have an undergrad degree in math. Remember, you will understand things better with each iteration so try to get some working understand in your first pass and also try to have a bird's eye view of what's going on. It is easy to get lost in the details.

I'm a math major studied in Canada. I am planning to do Financial Mathematic. I have talked to some professors from the Fin/Math department. They recommend me to take some thing like probability, real analysis, PDE, Functional Analysis. I would say it's a very tough program.

• Hi Phume, welcome to Academia.SE. Generally, answers should directly answer the question asked. This site is not for discussions but if you have something to add which does not answer the question, you should leave it as a comment under the question (I know that might be hard with too little reputation). Mar 23, 2014 at 22:43