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?

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    $\begingroup$ 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

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.

  • $\begingroup$ 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
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    $\begingroup$ non-linear programming is probably the most relevant for asset allocation $\endgroup$ – Mark Joshi Aug 7 '15 at 3:04

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