Discrete math -> math/comp finance

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How well would a background of studying subjects like discrete math, combinatorics, game theory, and optimization apply to working in computational or mathematical finance? I'm not considering doing this for the purpose of entering finance, I'm thinking of pursuing it to do research, but I'd like to know if finance would be a reasonable backup option if I ever decide to turn away from academia, and what kinds of positions/salaries I might expect to have available.

Think something like these: (not necessarily the actual PhD, maybe a similar program, or a combination of courses and self-studying that accomplish the same thing)

PhD Dual Degree in Algorithms, Combinatorics & Optimization | Tepper School of Business

GT Catalog : COC : School of Computer Science : PhD Program in Algorithms, Combinatorics, and Optimization ACO

Or the topics listed here: Research Guide - Machine Intelligence Research Institute

Thanks
 
what about the maths that is not 'discrete maths'?

What you describe is maths you learn in CS degrees? Most of it is not on the critical path (game theory??) IMO.
 
what about the maths that is not 'discrete maths'?

What you describe is maths you learn in CS degrees? Most of it is not on the critical path (game theory??) IMO.

Thanks for your reply - yeah, this misses a lot of the statistics, stochastic calculus, and other subjects which are prevalent in mathematical finance, but I was hoping that there might be smaller subfields where this type of knowledge is valuable.
 
Optimization might help, for example in portfolio construction
 
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