At Imandra (https://www.imandra.ai/) we've been collaborating with a few big names in finance, from our website: "In 2017 Aesthetic Integration partnered with Goldman Sachs to help deliver the SIGMA X MTF Auction Book, a new orderbook venue implementing periodic auctions. Aesthetic Integration used Imandra, our own automated reasoning engine, to formally model the Goldman Sachs design of the SIGMA X MTF Auction Book, verify its key properties, and automate rigorous testing. Now that the venue is live, Imandra is being used to perform ongoing validations of trading operations."

From what I've seen, most finance development seems to be "work hard not smart" – throw a lot of developers with a wide range of skill, poor development workflows, and QA at a problem, and then back them up with shifting the liability to someone else. This mostly works, it just costs a fortune and results in moving very slowly.

It depends on the stakes mainly, but also the experience of the stakeholders of a project. Both extremes (heavily tested, proven code vs "let's hope this works" code) are common but usually you're not allowed to speak about anything because of non-disclosure agreements and proven or not, all code is manually tested like crazy anyway. You commonly get insane overhead and just working code.