4
$\begingroup$

I'm currently a 2nd-year MS student in Mathematics at a mediocre state school. I'm planning to apply for the PHD programs in Operation Research/Financial Mathematics at schools like Columbia, Cornell, CMU, Georgia Tech, etc. I got straight As in Fourier Analysis (written by Elias Stein) and Linear Programming (written by I. Griva and A. Sofer) classes last year. For the incoming Fall semester, I currently consider taking 1 course out of the following, but not sure which one would benefit me the most for getting into one of the programs above:

  1. Nonlinear Programming - Linear and Nonlinear Optimization by A. Sofer and I. Griva

  2. Stochastic Processes - Introduction to Probability Models by Sheldon Cross

  3. Complex Analysis - Banach spaces of Analytic Functions by Keneth Hoffman

  4. Probability Theory - Probability by Alan Karr

I'm thinking of taking either $1$ or $3$, but I also saw that Stochastic Processes and Nonlinear Programming are core courses for the ORIE/ORFE programs at Columbia, Cornell, CMU, Georgia Tech, etc. Thus I am not entirely sure which one I should take to be well-prepared for such programs. Can anyone please give me some advice on which one of these $4$ courses should I absolutely need to take?

$\endgroup$
  • 1
    $\begingroup$ Well given that most of the universities apparently tell you explicitly that Stochastic Processes is a very important course, I'd say choose that... Also, I do not think that Complex Analysis, while very interesting, has much use in financial applications (could be mistaken though) $\endgroup$ – user2520938 Aug 6 '15 at 8:29
  • $\begingroup$ Thanks so much for your feedback. But how about Nonlinear Programming? It is also a core course required to take for those PhD programs in the 1st year (besides Linear Programming). And the universities don't "explicitly" say that, I just infer that information from the core courses listed by those universities. $\endgroup$ – user177196 Aug 6 '15 at 8:34
  • $\begingroup$ You could also consider following 2 courses. Given that you got As for some other courses I would imagine that you could successfully complete a semester while following one extra courses? $\endgroup$ – user2520938 Aug 6 '15 at 11:09
  • $\begingroup$ I can't, since I'm only allowed to take the maximum of 4 courses per semester. But I'm thinking between waiting to take the math class Stochastic DEs next spring vs taking an OR class Stochastic Processes this term. Any advice? $\endgroup$ – user177196 Aug 6 '15 at 19:52
0
$\begingroup$

financial maths tends to be applied stochastic processes so I'd regard that as most important. Probability is related.

Regression is used quite a lot in financial maths so linear programming is important too. Complex analysis is also useful for Fourier transform methods when doing pricing.

Non-linear programming I see as less important.

$\endgroup$
  • $\begingroup$ Thank you very much for your thought, Mr. Joshi (I love your book!). Based on your guidance, I should take stochastic processes, but for the sub-field of asset allocation/optimal portfolio allocation, is non-linear programming applied a lot? If not, which course should I take, besides Stochastic Processes, if I want to go deeply into this subfield? By the way, I read the syllabus of Stochastic Processes course at my school, and it seems to me it's basically a moderately high-level probability course, but not up to the stuffs using Lebesgue Measure theory, like a Probability class. $\endgroup$ – user177196 Aug 6 '15 at 17:38
  • $\begingroup$ And btw, between Stochastic Processes vs Stochastic Differential Equations, can I take the latter and forgo the former? $\endgroup$ – user177196 Aug 6 '15 at 17:44
  • $\begingroup$ it really depends on the subject content and which is at the right level for you. I'd find it odd if the school offered both and didn't have a preferred order of taking them, $\endgroup$ – Mark Joshi Aug 6 '15 at 20:58
  • $\begingroup$ a lot of asset allocation is quadratic programming so if that's what really interests you, do it. $\endgroup$ – Mark Joshi Aug 6 '15 at 21:00
  • 1
    $\begingroup$ non-linear programming is probably the most relevant for asset allocation $\endgroup$ – Mark Joshi Aug 7 '15 at 3:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.