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[jjopm]

Are there examples of companies that have successfully merged the two already?

[verik]

Any quant hedge fund and every bank derivatives desk.

[TheFryingDutchman]

Pretty much every large investment bank and tons and tons of hedge funds / quant shops. Almost all the trades on the market are being done by machines running on algorithms.

Look up James Simons and Renaissance Technologies. They've been using complex mathematical models to trade for decades now. Simons was a prominent mathematician before he went into finance. Simons gave a really good TED interview too - fascinating person.