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As a long practicing plasma physicist who moved into quantdom (now retired), I suggest focusing on stochastic calculus and modeling. How deep you go down the rabbit hole of measure theory will depend on what you do. Simulation will be your friend and help you in many situations. To the excellent suggestions above, I add Paul Glasserman's Monte Carlo Methods ...


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As a former physicist you will certainly enjoy Jean-Philippe Bouchaud’s approach. Pragmatic and empirical with simple models that are sophisticated enough to be useful. Check out “Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management” and “Trades, Quotes and Prices: Financial Markets Under the Microscope” in that ...


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Since you didn't study measure theoretic probability, that would be the first thing I recommend. In my opinion that's the main gap that many physicists on math side, because stochastic calculus is not in mainstream physics curriculum. Whether you first study measure theory in calculus then take on probability, or jump right into measure theoretic ...


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Physicists typically know PDEs but not stochastic calculus I have a masters in physics, so have a reasonable idea of the usual skillsets a physicist will know (at least at undergraduate level), and also then a masters in mathematical finance, so learnt the hard way the bits of maths physicists typically don't know but will need to know for quantitative ...


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It's not a great book, but Jan Dash. Quantitative Finance and Risk Management: A Physicist's Approach. World Scientific Publishing Company (2004) takes the approach that you might like - not too much formal math, and not too elementary.


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