As a long time practitioner I suggest some caution in the premise of your question, something which appears to have been overplayed in the popular press. Keep in mind the Levy Doob theorem, for instance, and the fact that arbitrage arguments are not the only structure giving rise to useful mathematics, even in the narrowest definition of this field (which I fear amounts to pricing PDEs in the minds of some, and within that the definition of an infinitesimal generator; and within that, a very small class of diffusion operators - you get my point). This has very limited relevance to credit risk, for example.
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