There have been Nobel Prize winning advances in Mathematical Finance but there is still work to be done. After putting on an initial delta hedge traders need to know when, and by how much, to adjust their hedge. Continuous time hedging is a mathematical fiction. “Hedge when you can, not when you have to” is a trader aphorism. Every trader knows after the first day on the job that you have to hedge when the market moves and if it is a big move you have to increase the volatility used for pricing.

My primitive thoughts on identifying the knobs that might be useful for quantifying this: https://keithalewis.github.io/math/um.html. Cash flows deserve equal footing with prices.

A complete theory should also involve the entities executing trades. Risk Management must include the hedging strategy used to mitigate risk and identifiy who gets to decide what trades to execute: https://keithalewis.github.io/math/uf.html. The theory must allow for not all market participants behaving optimally.

What I don’t know fills almost the entire universe. Feedback welcome.

If you know Excel and C++ you might like https://xlladdins.com.