- "The Evaluation and Optimization of Trading Strategies" by Pardo
- "The Elements of Statistical Learning" by Hastie et al
- "The Evaluation and Optimization of Trading Strategies" by Pardo
- "The Elements of Statistical Learning" by Hastie et al
I haven't really had much use for math in algo trading so far. I get ideas from looking at historical chart data, code up a base algorithm which implements an idea, and use genetic algorithms to find optimal values for range-bound variables (e.g., a float between 0.995 and 0.997) in the "optimization" step of WFA. I then run WFA across my defined in and out of sample periods on historical tick data directly from my broker (a few gb per year per symbol).
The most complex math I've done in trading so far has been writing some R scripts to generate pretty graphs. It's a stretch to call that "math", though.
WFA completely changed the game for me. I was aware of curve fitting and tried to avoid it before, but after reading about WFA it was like the wool covering was removed from my eyes...
Any suggestions on applied math? I suspect I just haven't been exposed to enough of it to really connect the theory to the real world.
With experience and practice with theoretical math, you also learn how to apply it.
Tool makers have more insight into the assumptions behind the tools they create -- they might know how a tool was meant to be used and what its limits are. That being said, there are times when using a screwdriver as a hammer is expedient and does no harm. Of course, there are other times where using Black-Scholes to model a high-volatility market outside of the 'smoothly differentiable' market assumptions it was built on can crash a large part of the economy. It can be a dangerous game to use someone else's tools without knowing their assumptions.
As for applied math suggestions:
1) Watch Feynman's take on applied math in physics: https://www.youtube.com/watch?v=obCjODeoLVw
2) Read this essay "A Mathematician's Lament" which points out the math learned in school is likely not really mathematics and that surprisingly math is not practical but aesthetic -- mathematics is closer to art than we are taught: http://www.maa.org/external_archive/devlin/LockhartsLament.p...