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Of course it is fast enough. But what is fast enough? I know guys who trade off Excel sheets and they make millions, but those guys are clearly not active in high frequency space. So, it entirely depends on your trading frequency and average holding period. I also know of shops that run live trading systems by calling R functions, so, obviously Matlab ...

If I understand you right, you are talking specifically about Matlab's embedded code generation facility (see here: http://www.mathworks.ch/embedded-code-generation/). In my view, the answer to your question is clearly yes. This feature allows you to generate hardware specific code, e.g. for deployment on GPU's (video cards). It's used for aerospace ...

No, rng does not do the same as rand. rng sets the seed for the random number generator and rand generates random numbers. Also it can be seen in documentation that the rng function only accepts positive integers. Usually random number generator algorithms start with integers for the seed. For various examples: C random function takes the system clock as ...